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product (Ghostscript) search {pop pop pop revision 927 gt}{pop false} ifelse{/BorderArrayPatch{} def}{/BorderArrayPatch{[exch{dup dup type/integertype eq exch type/realtype eq or{BPToDvips}if}forall]}def} ifelse /HyperBorder {1 PDFToDvips} def/H.V {pdf@hoff pdf@voff null} def/H.B {/Rect[pdf@llx pdf@lly pdf@urx pdf@ury]} def/H.S {currentpoint HyperBorder add /pdf@lly exch def dup DvipsToPDF 72 add /pdf@hoff exch def HyperBorder sub /pdf@llx exch def} def/H.L {2 sub dup/HyperBasePt exch def PDFToDvips /HyperBaseDvips exch def currentpoint HyperBaseDvips sub /pdf@ury exch def/pdf@urx exch def} def/H.A {H.L currentpoint exch pop vsize 72 sub exch DvipsToPDF HyperBasePt sub sub /pdf@voff exch def} def/H.R {currentpoint HyperBorder sub /pdf@ury exch def HyperBorder add /pdf@urx exch def currentpoint exch pop vsize 72 sub exch DvipsToPDF sub /pdf@voff exch def} def /pgfHrgb{/pgfheight exch def 0.75 setlinewidth [] 0 setdash /pgfshade {pgfArgb} def /pgfdir { dup 0 moveto dup 5 index lineto } bind def} bind def /pgfVrgb{/pgfheight exch def 0.75 setlinewidth [] 0 setdash /pgfshade {pgfArgb} def /pgfdir { dup 0 exch moveto dup 5 index exch lineto } bind def} bind def /pgfArgb{ /pgfdiff 8 index round cvi 8 index round cvi sub 2 mul 1 add def 2 index 6 index sub pgfdiff div 2 index 6 index sub pgfdiff div 2 index 6 index sub pgfdiff div pgfheight 9 index 9 index 9 index 14 index pgfdiff { 3 index 3 index 3 index setrgbcolor pgfdir stroke 4 -1 roll 7 index add 4 -1 roll 6 index add 4 -1 roll 5 index add 4 -1 roll .5 sub } repeat mark 15 1 roll cleartomark exch pop }bind def /pgfR1rgb{ newpath dup dup dup 0 360 arc clip newpath dup /pgfendx exch def /pgfendy exch def 0.875 setlinewidth [] 0 setdash /pgfshade {pgfRrgb} def /pgfstartx exch def /pgfstarty exch def /pgfdiffx pgfendx pgfstartx sub def /pgfdiffy pgfendy pgfstarty sub def dup /pgfdomb exch def }bind def /pgfR2rgb{ newpath 0.5 add pgfcircx pgfcircy 3 2 roll 0 360 arc setrgbcolor fill pop}bind def /pgfRrgb{ /pgfdiff 8 index round cvi 8 index round cvi sub 4 mul 1 add def /pgfcircx pgfstartx 9 index pgfdiffx pgfdomb div mul add def /pgfcircy pgfstarty 9 index pgfdiffy pgfdomb div mul add def /pgfcircxe pgfstartx 8 index pgfdiffx pgfdomb div mul add def /pgfcircye pgfstarty 8 index pgfdiffy pgfdomb div mul add def /pgfxstep pgfcircxe pgfcircx sub pgfdiff div def /pgfystep pgfcircye pgfcircy sub pgfdiff div def 2 index 6 index sub pgfdiff div 2 index 6 index sub pgfdiff div 2 index 6 index sub pgfdiff div 8 index 8 index 8 index 13 index pgfdiff { 3 index 3 index 3 index setrgbcolor pgfcircx pgfcircy 2 index 0 360 arc closepath stroke 4 -1 roll 6 index add 4 -1 roll 5 index add 4 -1 roll 4 index add 4 -1 roll .25 sub /pgfcircx pgfcircx pgfxstep add def /pgfcircy pgfcircy pgfystep add def } repeat mark 14 1 roll cleartomark exch pop }bind def /pgfHcmyk{ /pgfheight exch def 0.75 setlinewidth [] 0 setdash /pgfshade {pgfAcmyk} def /pgfdir { dup 0 moveto dup 6 index lineto } bind def} bind def /pgfVcmyk{ 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setcmykcolor fill pop}bind def /pgfRcmyk{ /pgfdiff 10 index round cvi 10 index round cvi sub 4 mul 1 add def /pgfcircx pgfstartx 11 index pgfdiffx pgfdomb div mul add def /pgfcircy pgfstarty 11 index pgfdiffy pgfdomb div mul add def /pgfcircxe pgfstartx 10 index pgfdiffx pgfdomb div mul add def /pgfcircye pgfstarty 10 index pgfdiffy pgfdomb div mul add def /pgfxstep pgfcircxe pgfcircx sub pgfdiff div def /pgfystep pgfcircye pgfcircy sub pgfdiff div def 3 index 8 index sub pgfdiff div 3 index 8 index sub pgfdiff div 3 index 8 index sub pgfdiff div 3 index 8 index sub pgfdiff div 11 index 11 index 11 index 11 index 17 index pgfdiff { 4 index 4 index 4 index 4 index setcmykcolor pgfcircx pgfcircy 2 index 0 360 arc closepath stroke 5 -1 roll 8 index add 5 -1 roll 7 index add 5 -1 roll 6 index add 5 -1 roll 5 index add 5 -1 roll .25 sub /pgfcircx pgfcircx pgfxstep add def /pgfcircy pgfcircy pgfystep add def } repeat mark 18 1 roll cleartomark exch pop }bind def /pgfHgray{ /pgfheight exch 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/pgfcircx pgfstartx 5 index pgfdiffx pgfdomb div mul add def /pgfcircy pgfstarty 5 index pgfdiffy pgfdomb div mul add def /pgfcircxe pgfstartx 4 index pgfdiffx pgfdomb div mul add def /pgfcircye pgfstarty 4 index pgfdiffy pgfdomb div mul add def /pgfxstep pgfcircxe pgfcircx sub pgfdiff div def /pgfystep pgfcircye pgfcircy sub pgfdiff div def dup 2 index sub pgfdiff div 2 index 5 index pgfdiff { 1 index setgray pgfcircx pgfcircy 2 index 0 360 arc closepath stroke exch 2 index add exch .25 sub /pgfcircx pgfcircx pgfxstep add def /pgfcircy pgfcircy pgfystep add def } repeat mark 6 1 roll cleartomark exch pop }bind def /pgfsc{}bind def/pgffc{}bind def/pgfstr{stroke}bind def/pgffill{fill}bind def/pgfeofill{eofill}bind def/pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def/pgfw{setlinewidth}bind def/pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale magscale{1 DVImag div dup scale}if pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def/pgfr{pgfsd restore}bind def userdict begin/pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def /pgfc{newpath @endspecial pgfpd}bind def /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def/pgfpd{/delta globaldict /pgfdelta get def}bind def /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse /.pgfsetfillopacityalpha{/pgffoa exch def /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def /pgffoa 1 def /pgfsoa 1 def end /pgf1{gsave exec 1.0 pgfw 2.00002 0.0 moveto -6.00006 4.00005 lineto -3.00003 0.0 lineto -6.00006 -4.00005 lineto pgffill grestore} bind def /pgf2{gsave exec 1.0 pgfw 0.8 pgfw [ ] 0.0 setdash 1 setlinecap 1 setlinejoin -3.00003 4.00005 moveto 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cleartomark %%EndFont %%BeginFont: TeX-mathx10 %!PS-AdobeFont-1.0: TeX-mathx10 001.001 % Filtered by type1fix.pl 0.08 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright 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-1.91284 -2.55046 lineto pgffill restore restore 0 TeXcolorgray restore save save [1.0 0.0 0.0 1.0 -35.22704 -103.83603 ] concat pgfs 1643 1607 a 0 setgray 1643 1607 a 0.5 TeXcolorgray Fn(x)1687 1615 y Fl(i)1734 1607 y Fo(\020)g Fn(\016)s(i;)91 b Fo(|)p Fn(i)p Fo(|)22 b(\244)f Fn(N)p 0 TeXcolorgray 1643 1607 a pgfr restore restore save [ 0.79701 1.99255 ] 0.0 setdash 0.79701 pgfw 0 TeXcolorgray 63.49677 0.0 moveto 63.49677 0.0 64.86201 1.36523 65.38638 1.88959 curveto 65.91072 2.41393 66.75162 3.25482 67.27599 3.77917 curveto 67.80032 4.30353 68.64122 5.14444 69.16557 5.66878 curveto 69.68993 6.19313 70.53084 7.03404 71.05518 7.55838 curveto 71.57953 8.08273 72.42043 8.92365 72.94476 9.448 curveto 73.46913 9.97234 74.31003 10.81323 74.83438 11.33759 curveto 75.35873 11.86192 76.19963 12.70282 76.72398 13.22719 curveto 77.24832 13.75154 78.08923 14.59245 78.61357 15.11679 curveto 79.13792 15.64114 79.97884 16.48204 80.50317 17.00638 curveto 81.02753 17.53073 81.86844 18.37164 82.39279 18.896 curveto 82.91713 19.42033 83.75804 20.26123 84.2824 20.78558 curveto 84.80673 21.30994 85.64763 22.15083 86.17198 22.6752 curveto 86.69633 23.19955 87.53725 24.04045 88.06158 24.56479 curveto 88.58594 25.08914 89.42683 25.93004 89.95119 26.45439 curveto 90.47554 26.97873 91.31644 27.81964 91.84079 28.344 curveto 92.36513 28.86833 93.20604 29.70924 93.7304 30.2336 curveto 94.25473 30.75795 95.09563 31.59886 95.61998 32.1232 curveto 96.14435 32.64755 96.98524 33.48845 97.5096 34.01279 curveto 98.03395 34.53714 98.87485 35.37805 99.39919 35.9024 curveto 99.92354 36.42674 100.76445 37.26765 101.2888 37.792 curveto 101.81314 38.31635 102.65404 39.15724 103.17839 39.6816 curveto 103.70273 40.20595 104.54366 41.04686 105.068 41.5712 curveto 105.59235 42.09555 106.43326 42.93645 106.9576 43.46078 curveto 107.48195 43.98515 108.8472 45.35042 108.8472 45.35042 curveto pgfstr 0 TeXcolorgray restore save [ 0.79701 1.99255 ] 0.0 setdash 0.79701 pgfw 0 TeXcolorgray -108.85162 -45.35484 moveto 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-17.53517 -80.50761 -17.01082 curveto -79.98326 -16.48648 -79.14236 -15.64557 -78.61801 -15.12122 curveto -78.09366 -14.59688 -77.25275 -13.75597 -76.72841 -13.23161 curveto -76.20406 -12.70726 -75.36316 -11.86636 -74.83882 -11.34201 curveto -74.31447 -10.81766 -73.47356 -9.97676 -72.9492 -9.45241 curveto -72.42487 -8.92807 -71.58395 -8.08716 -71.0596 -7.5628 curveto -70.53526 -7.03847 -69.69437 -6.19757 -69.17001 -5.67322 curveto -68.64566 -5.14885 -67.80475 -4.30795 -67.28041 -3.78362 curveto -66.75606 -3.25926 -65.91516 -2.41835 -65.39081 -1.89401 curveto -64.86646 -1.36966 -63.50119 -0.00441 -63.50119 -0.00441 curveto pgfstr 0 TeXcolorgray restore save save [1.0 0.0 0.0 1.0 58.04605 -8.4328 ] concat pgfs 1643 1607 a 0 setgray 1643 1607 a FD(\026)1693 1619 y FG(d)1643 1607 y pgfr restore restore save 0 TeXcolorgray 63.49677 0.0 moveto 65.12947 0.0 moveto 65.12947 0.90172 64.3985 1.63269 63.49677 1.63269 curveto 62.59505 1.63269 61.86407 0.90172 61.86407 0.0 curveto 61.86407 -0.90172 62.59505 -1.63269 63.49677 -1.63269 curveto 64.3985 -1.63269 65.12947 -0.90172 65.12947 0.0 curveto closepath 63.49677 0.0 moveto pgfstr 0 TeXcolorgray restore save 0 TeXcolorgray -63.49677 0.0 moveto -61.86407 0.0 moveto -61.86407 0.90172 -62.59505 1.63269 -63.49677 1.63269 curveto -64.3985 1.63269 -65.12947 0.90172 -65.12947 0.0 curveto -65.12947 -0.90172 -64.3985 -1.63269 -63.49677 -1.63269 curveto -62.59505 -1.63269 -61.86407 -0.90172 -61.86407 0.0 curveto closepath -63.49677 0.0 moveto pgfstr 0 TeXcolorgray restore save 0 TeXcolorgray 81.63872 0.0 moveto 83.81566 0.0 moveto 83.81566 1.20229 82.84102 2.17693 81.63872 2.17693 curveto 80.43643 2.17693 79.46178 1.20229 79.46178 0.0 curveto 79.46178 -1.20229 80.43643 -2.17693 81.63872 -2.17693 curveto 82.84102 -2.17693 83.81566 -1.20229 83.81566 0.0 curveto closepath 81.63872 0.0 moveto pgfstr 0 TeXcolorgray restore save 1 TeXcolorgray 81.63872 0.0 moveto 83.81566 0.0 moveto 83.81566 1.20229 82.84102 2.17693 81.63872 2.17693 curveto 80.43643 2.17693 79.46178 1.20229 79.46178 0.0 curveto 79.46178 -1.20229 80.43643 -2.17693 81.63872 -2.17693 curveto 82.84102 -2.17693 83.81566 -1.20229 83.81566 0.0 curveto closepath 81.63872 0.0 moveto pgffill 0 TeXcolorgray restore save 0 TeXcolorgray -81.63872 0.0 moveto -79.46178 0.0 moveto -79.46178 1.20229 -80.43643 2.17693 -81.63872 2.17693 curveto -82.84102 2.17693 -83.81566 1.20229 -83.81566 0.0 curveto -83.81566 -1.20229 -82.84102 -2.17693 -81.63872 -2.17693 curveto -80.43643 -2.17693 -79.46178 -1.20229 -79.46178 0.0 curveto closepath -81.63872 0.0 moveto pgfstr 0 TeXcolorgray restore save 1 TeXcolorgray -81.63872 0.0 moveto -79.46178 0.0 moveto -79.46178 1.20229 -80.43643 2.17693 -81.63872 2.17693 curveto -82.84102 2.17693 -83.81566 1.20229 -83.81566 0.0 curveto -83.81566 -1.20229 -82.84102 -2.17693 -81.63872 -2.17693 curveto -80.43643 -2.17693 -79.46178 -1.20229 -79.46178 0.0 curveto closepath -81.63872 0.0 moveto pgffill 0 TeXcolorgray restore save save [1.0 0.0 0.0 1.0 -72.82095 5.32843 ] concat pgfs 1643 1607 a 0 setgray 1643 1607 a FB(\001)p FD(\026)1758 1619 y FG(d)1643 1607 y pgfr restore restore save 0.79701 pgfw 0 TeXcolorgray -54.42581 -1.27005 moveto -54.42581 1.27005 lineto pgfstr 0 TeXcolorgray restore save save [1.0 0.0 0.0 1.0 -90.34091 5.32843 ] concat pgfs 1643 1607 a 0 setgray 1643 1607 a FB(\001)p FD(\026)1758 1619 y FG(s)1643 1607 y pgfr restore restore save 0.79701 pgfw 0 TeXcolorgray -81.63872 -1.27005 moveto -81.63872 1.27005 lineto pgfstr 0 TeXcolorgray restore save save [1.0 0.0 0.0 1.0 76.81 -8.4328 ] concat pgfs 1643 1607 a 0 setgray 1643 1607 a FD(\026)1693 1619 y FG(s)1643 1607 y pgfr restore restore save 0.79701 pgfw 0 TeXcolorgray 81.63872 -1.27005 moveto 81.63872 1.27005 lineto pgfstr 0 TeXcolorgray restore save 0 0 1 TeXcolorrgb [ 2.98883 1.99255 0.3985 1.99255 ] 0.0 setdash 99.78065 -21.77026 moveto 99.78065 21.31198 lineto pgfstr save [0.0 1.0 -1.0 0.0 99.78065 21.31198 ] concat save 0.31879 pgfw [ ] 0.0 setdash 1 setlinecap 1 setlinejoin -1.19551 1.59401 moveto -1.09587 0.99626 0.0 0.09961 0.29886 0.0 curveto 0.0 -0.09961 -1.09587 -0.99626 -1.19551 -1.59401 curveto pgfstr restore restore 0 TeXcolorgray restore save 0 0 1 TeXcolorrgb [ 2.98883 1.99255 0.3985 1.99255 ] 0.0 setdash -45.35484 -45.35484 moveto -45.35484 -9.52924 lineto pgfstr save [0.0 1.0 -1.0 0.0 -45.35484 -9.52924 ] concat save 0.31879 pgfw [ ] 0.0 setdash 1 setlinecap 1 setlinejoin -1.19551 1.59401 moveto -1.09587 0.99626 0.0 0.09961 0.29886 0.0 curveto 0.0 -0.09961 -1.09587 -0.99626 -1.19551 -1.59401 curveto pgfstr restore restore 0 TeXcolorgray restore save 0 0 1 TeXcolorrgb [ 2.98883 1.99255 0.3985 1.99255 ] 0.0 setdash -9.07095 -45.35484 moveto -9.07095 -9.52924 lineto pgfstr save [0.0 1.0 -1.0 0.0 -9.07095 -9.52924 ] concat save 0.31879 pgfw [ ] 0.0 setdash 1 setlinecap 1 setlinejoin -1.19551 1.59401 moveto -1.09587 0.99626 0.0 0.09961 0.29886 0.0 curveto 0.0 -0.09961 -1.09587 -0.99626 -1.19551 -1.59401 curveto pgfstr restore restore 0 TeXcolorgray restore save 0 0 1 TeXcolorrgb [ 2.98883 1.99255 0.3985 1.99255 ] 0.0 setdash 27.21289 -45.35484 moveto 27.21289 -9.52924 lineto pgfstr save [0.0 1.0 -1.0 0.0 27.21289 -9.52924 ] concat save 0.31879 pgfw [ ] 0.0 setdash 1 setlinecap 1 setlinejoin -1.19551 1.59401 moveto -1.09587 0.99626 0.0 0.09961 0.29886 0.0 curveto 0.0 -0.09961 -1.09587 -0.99626 -1.19551 -1.59401 curveto pgfstr restore restore 0 TeXcolorgray restore save 0 0 1 TeXcolorrgb [ 2.98883 1.99255 0.3985 1.99255 ] 0.0 setdash 63.49677 -63.49677 moveto 63.49677 -27.67117 lineto pgfstr save [0.0 1.0 -1.0 0.0 63.49677 -27.67117 ] concat save 0.31879 pgfw [ ] 0.0 setdash 1 setlinecap 1 setlinejoin -1.19551 1.59401 moveto -1.09587 0.99626 0.0 0.09961 0.29886 0.0 curveto 0.0 -0.09961 -1.09587 -0.99626 -1.19551 -1.59401 curveto pgfstr restore restore 0 TeXcolorgray restore save 0 0 1 TeXcolorrgb [ 2.98883 1.99255 0.3985 1.99255 ] 0.0 setdash -81.63872 -68.9394 moveto -81.63872 -33.11382 lineto pgfstr 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v 891 1311 5 47 v 924 1311 V 891 1316 39 5 v 929 1316 a SDict begin H.S end 929 1316 a 929 1316 a SDict begin 12 H.A end 929 1316 a 929 1316 a SDict begin [/View [/XYZ H.V]/Dest (thm.2.2) cvn /DEST pdfmark end 929 1316 a 150 1432 a Fg(Remark)d(2.2.)38 b Fz(A)n(n)22 b(essential)i(ingr)l(e)l(dient)f(of)h(the)g(pr)l(o)l(of)g (is)g(the)f(c)l(ontinuity)g(of)h(the)f(mapping)0 1532 y FD(X)76 1502 y Fy(\016)135 1532 y FB(\321)h FD(V)308 1502 y Fy(\016)375 1532 y Fz(thr)l(ough)30 b(\(2.5\).)41 b(When)30 b FD(\026)1206 1544 y FG(d)1270 1532 y FB(\240)23 b FD(\026)1408 1544 y FG(s)1438 1532 y Fz(,)31 b(the)f(way)h(to)f (de\014ne)g(the)g(mapping)h(do)l(es)g(not)f(r)l(ely)0 1631 y(on)39 b(a)f(monotone)h(maximal)g(multivalue)l(d)g(op)l(er)l (ator)h([)p 0 0 0.6 TeXcolorrgb 1754 1631 a SDict begin H.S end 1754 1631 a 0 0 0.6 TeXcolorrgb Fz(9)p 0 0 0.6 TeXcolorrgb 1796 1578 a SDict begin H.R end 1796 1578 a 1796 1631 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.brezis73) cvn H.B /ANN pdfmark end 1796 1631 a 0 TeXcolorgray Fz(])g(\(r)l(eplacing)g FB(B)s FD(')p Fz(\).)64 b(Such)39 b(a)f(mapping)0 1731 y(c)l(an)g(b)l(e)f(de\014ne)l(d)h(using)g(an)g (EVI)f(appr)l(o)l(ach)j([)p 0 0 0.6 TeXcolorrgb 1481 1731 a SDict begin H.S end 1481 1731 a 0 0 0.6 TeXcolorrgb Fz(5)p 0 0 0.6 TeXcolorrgb 1523 1677 a SDict begin H.R end 1523 1677 a 1523 1731 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.BBCMM21) cvn H.B /ANN pdfmark end 1523 1731 a 0 TeXcolorgray Fz(],)i(however)d(it)e(is)h(not)g(c)l(ontinuous)f (in)g(gener)l(al)0 1831 y(\(shown)32 b(b)l(elow\).)45 b(This)32 b(explains)h(why)f(c)l(onver)l(genc)l(e)g(of)g(the)g(system)f (holds)i(only)f(for)g FD(\026)2811 1843 y FG(d)2878 1831 y FB(\020)26 b FD(\026)3019 1843 y FG(s)3050 1831 y Fz(.)0 1930 y(In)41 b(the)g(EVI)g(fr)l(amework,)46 b(for)c(any)f(c)l (ontinuous)g(function)g FD(x)p FB(p\004q)p Fz(,)k(the)c(mapping)i(pr)l (o)l(duc)l(es)f(a)0 2030 y(function)g FD(v)s FB(p\004q)g Fz(for)g(which)i(the)d(phases)56 b FC(9)-36 b FD(v)30 b FB(\010)d FD(\026)1537 2042 y FG(d)1578 2030 y Fz(sign)p FB(p)p FD(v)s FB(q)45 b(\020)p 0 TeXcolorgray 44 w Fs(b)p FB(p)p FD(v)s FB(q)19 b(\000)f FD(x)p 0 TeXcolorgray 42 w Fz(and)p 0 TeXcolorgray 42 w FB(|)p Fs(b)p FB(p)p FE(0)p FB(q)g(\000)g FD(x)p FB(|)p 0 TeXcolorgray 45 w(\244)45 b FD(\026)3045 2042 y FG(s)0 2129 y Fz(o)l(c)l(cur)37 b(when)h FB(\010)p FD(v)i FB(\241)c FE(0)h Fz(and)h FD(v)j FB(\020)36 b FE(0)p Fz(,)j(r)l(esp)l(e)l(ctively,)i(on)d(non-empty)f (time)h(intervals.)62 b(T)-6 b(o)38 b(se)l(e)0 2229 y(that)30 b(such)g(a)g(mapping)i FD(x)23 b FB(\336\321)h FD(v)s FB(p)p FD(x)p FB(q)31 b Fz(is)f(not)g(c)l(ontinuous)f(in)h(gener)l(al,) h(we)f(c)l(onsider)h(for)g(instanc)l(e)0 2329 y FD(b)p FB(p)p FD(x;)14 b(v)s FB(q)40 b(\020)f FD(x)h Fz(and)f FD(v)s FB(p)p FE(0)p FB(q)h(\020)f FE(0)p Fz(.)66 b(If)39 b FB(@)p FD(t)g FB(\245)g FE(0)p FD(;)14 b(x)p FB(p)p FD(t)p FB(q)40 b(\020)g FD(\026)1785 2341 y FG(s)1854 2329 y Fz(then)f FB(@)p FD(t)g FB(\245)g FE(0)p FD(;)14 b(v)s FB(p)p FD(t)p FB(q)40 b(\020)f FE(0)f Fz(wher)l(e)l(as)i(if)0 2428 y FB(@)p FD(t)23 b FB(\245)g FE(0)p FD(;)14 b(x)314 2398 y Fy(\017)345 2428 y FB(p)p FD(t)p FB(q)24 b(\020)f FD(\026)601 2440 y FG(s)649 2428 y FB(\000)18 b(p)p FD(\017)h FB(\001)f FD(t)p FB(q)p FJ(1)1010 2444 y Fy(t)p Fx(Pr)p FG(0)p Fy(;\017)p Fx(s)1230 2428 y Fz(then)30 b FB(@)p FD(t)23 b FB(\245)f FE(0)p FD(;)14 b(v)1724 2398 y Fy(\017)1756 2428 y FB(p)p FD(t)p FB(q)24 b(\020)e(p)p FD(\026)2043 2440 y FG(s)2092 2428 y FB(\001)c FD(\026)2225 2440 y FG(d)2266 2428 y FB(q)p FD(t)h FB(\000)f FD(\017)p FB(p)p FD(\017)g FB(^)g FD(t)p FB(q)2707 2360 y Fr(\000)2745 2428 y FE(1)g FB(\001)2898 2396 y Fy(t)p Fx(^)p Fy(\017)p 2898 2410 104 4 v 2933 2457 a FG(2)3011 2360 y Fr(\010)3050 2428 y Fz(.)0 2528 y(Ther)l(efor)l(e)31 b(it)e(is)g(cle)l(ar)h(that)k FE(lim)914 2579 y Fy(\017)p Fx(\321)p FG(0)1054 2528 y FB(})p FD(x)16 b FB(\001)h FD(x)1281 2498 y Fy(\017)1313 2528 y FB(})23 b(\020)f FE(0)29 b Fz(but)k FE(lim)1668 2579 y Fy(\017)p Fx(\321)p FG(0)1808 2528 y FB(})p FD(v)20 b FB(\001)c FD(v)2027 2498 y Fy(\017)2059 2528 y FB(})23 b(\020)f(p)p FD(\026)2286 2540 y FG(s)2334 2528 y FB(\001)16 b FD(\026)2465 2540 y FG(d)2506 2528 y FB(q)p FD(T)40 b Fz(wher)l(e)30 b FB(})16 b(\004)h(})29 b Fz(is)0 2658 y(the)h(max)f(norm)h(on)g FB(r)p FE(0)p FD(;)14 b(T)e FB(s)p Fz(.)0 2758 y FE(The)28 b(state)f(space)g(of)g(the)h(pro)r(cess) f Fh(Z)1193 2728 y Fy(\016)1257 2758 y FE(is)726 2974 y SDict begin H.S end 726 2974 a 726 2974 a SDict begin 12 H.A end 726 2974 a 726 2974 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.7) cvn /DEST pdfmark end 726 2974 a FD(E)h FB(\020)979 2895 y Fr(\244)903 3075 y Fx(p)p Fy(x;y)r Fx(qP)p Ff(S)1121 3058 y Fp(\016)1161 2974 y FD(E)1222 2986 y Fy(x;y)1320 2974 y FD(;)180 b(E)1584 2986 y Fy(x;y)1704 2974 y FB(\020)23 b(tp)p FD(x;)14 b(y)s FB(qu)19 b(\002)f FD(H)2229 2986 y Fy(x;y)2326 2974 y FD(;)555 b FE(\(2.7\))0 3293 y(where)18 b FA(S)283 3262 y Fy(\016)336 3293 y FB(\020)23 b(t)p FD(x)508 3305 y Fx(\001)p Fy(N)622 3293 y FD(;)14 b(:)g(:)g(:)g(;)g(x)854 3305 y Fx(\001)p Fy(k)940 3313 y Fp(\026)975 3321 y Fq(s)1007 3305 y Fx(\001)p FG(1)1095 3293 y FB(u\002t\001)p FE(1)p FD(;)g FE(1)p FB(uYt)p FD(x)1606 3305 y Fx(\001)p Fy(k)1692 3313 y Fp(\026)1727 3321 y Fq(s)1760 3293 y FD(;)g(:)g(:)g(:)g(;)g(x) 1992 3305 y Fy(k)2027 3313 y Fp(\026)2062 3321 y Fq(s)2098 3293 y FB(u\002t\001)p FE(1)p FD(;)g FE(0)p FD(;)g FE(1)p FB(uYt)p FD(x)2688 3305 y Fy(k)2723 3313 y Fp(\026)2758 3321 y Fq(s)2787 3305 y Fx(\000)p FG(1)2875 3293 y FD(;)g(:)g(:)g(:)g (;)g(x)3107 3305 y Fy(N)3170 3293 y FB(u\002)0 3392 y(t\001)p FE(1)p FD(;)g FE(1)p FB(u)p FE(,)47 b FD(H)399 3404 y Fy(x;y)548 3392 y FB(\020)j(p\0018)p FD(;)14 b FE(0)p FB(q)44 b FE(if)g FB(p)p FD(x;)14 b(y)s FB(q)52 b(P)f(t)p FD(x)1504 3404 y Fx(\001)p Fy(k)1590 3412 y Fp(\026)1625 3420 y Fq(s)1661 3392 y FD(;)14 b(:)g(:)g(:)g(;)g(x)1893 3404 y Fy(N)1956 3392 y FB(u)30 b(\002)f(t\001)p FE(1)p FB(u)p FE(,)47 b FD(H)2437 3404 y Fy(x;y)2586 3392 y FB(\020)k(p)p FE(0)p FD(;)14 b FB(\0008q)44 b FE(if)0 3492 y FB(p)p FD(x;)14 b(y)s FB(q)44 b(P)f(t)p FD(x)407 3504 y Fx(\001)p Fy(N)521 3492 y FD(;)14 b(:)g(:)g(:)f(;)h(x)752 3504 y Fy(k)787 3512 y Fp(\026)822 3520 y Fq(s)859 3492 y FB(u)26 b(\002)g(t)p FE(1)p FB(u)p FE(,)42 b(and)d FD(H)1436 3504 y Fy(x;y)1577 3492 y FB(\020)j FA(R)k FE(otherwise.)71 b(Let)40 b Fe(E)47 b FE(denote)39 b(the)h(class)0 3591 y(of)28 b(measurable)c(sets)j(in)g FD(E)5 b FE(:)880 3808 y SDict begin H.S end 880 3808 a 880 3808 a SDict begin 12 H.A end 880 3808 a 880 3808 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.8) cvn /DEST pdfmark end 880 3808 a Fe(E)31 b FB(\020)22 b FD(\033)1092 3739 y Fr(\000)1131 3808 y FD(A)1193 3820 y Fy(x;y)1290 3808 y FD(;)28 b(A)1403 3820 y Fy(x;y)1524 3808 y FB(P)22 b Fe(E)1634 3820 y Fy(x;y)1732 3808 y FD(;)14 b FB(p)p FD(x;)g(y)s FB(q)23 b(P)g FA(S)2103 3773 y Fy(\016)2134 3739 y Fr(\010)2172 3808 y FD(;)709 b FE(\(2.8\))0 4024 y(where)27 b Fe(E)284 4036 y Fy(x;y)409 4024 y FE(denotes)g(the)h(Borel)e(sets)h(of)g FD(E)1390 4036 y Fy(x;y)1488 4024 y FE(.)150 4140 y(The)h(Mark)n(o)n(v) d(ev)n(olution)g(of)i Fh(Z)1147 4110 y Fy(\016)1211 4140 y FE(is)g(determined)f(b)n(y)h(the)h(follo)n(wing)23 b(ob)5 b(jects:)0 4240 y(-)27 b(the)h(real-v)-5 b(alued)25 b(and)i(smo)r(oth)f(v)n(ectors)g(\014elds)h FD(B)t FB(p)p Fh(z)s FB(q)p FE(,)i Fh(z)e FB(\020)22 b(p)p FD(x;)14 b(y)s(;)g(v)s FB(q)p FE(,)29 b(giv)n(en)d(b)n(y)74 4456 y SDict begin H.S end 74 4456 a 74 4456 a SDict begin 12 H.A end 74 4456 a 74 4456 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.9) cvn /DEST pdfmark end 74 4456 a FD(B)t FB(p)p FD(x;)14 b FB(\001)p FE(1)p FD(;)g(v)s FB(q)23 b(\020)g FD(\026)637 4468 y FG(d)696 4456 y FB(\000)p 0 TeXcolorgray 18 w Fs(b)p FB(p)p FD(v)s FB(q)c(\000)f FD(x)p 0 TeXcolorgray(;)180 b(B)t FB(p)p FD(x;)14 b FE(0)p FD(;)g(v)s 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FB(q)c(\020)e(\001)p FD(v)s FE(\),)0 4954 y(-)27 b(the)h(constan)n(t)f(rate)g(function)g(\003)c FB(\020)g FE(2)p FD(\034)1285 4924 y Fx(\001)p FG(2)1373 4954 y FD(\016)1413 4924 y Fx(\001)p FG(2)1501 4954 y FE(,)0 5053 y(-)31 b(the)i(probabilit)n(y)27 b(transition)i(measure)h Fe(Q)f FE(:)h Fe(E)f FB(\002)p 1655 4987 67 4 v 21 w FD(E)35 b FB(\321)29 b(r)p FE(0)p FD(;)14 b FE(1)p FB(s)30 b FE(is)h(discrete)f(b)r(ecause)h FD(V)2847 5023 y Fy(\016)2915 5053 y FE(do)r(es)0 5153 y(not)d(jump:)p 0 TeXcolorgray 0 TeXcolorgray eop end end %%Page: 7 7 TeXDict begin HPSdict begin 7 6 bop 0 TeXcolorgray 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a 0 TeXcolorgray -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest 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FD(x)975 489 y Fx(\001)p Fy(N)1089 477 y FD(;)14 b(:)g(:)g(:)g(;)g(x) 1321 489 y Fx(\001)p Fy(k)1407 497 y Fp(\026)1442 505 y Fq(s)1474 489 y Fx(\001)p FG(1)1562 477 y FB(u)p FD(;)32 b Fe(Q)1722 409 y Fr(\000)1760 477 y FB(p)p FD(x;)14 b FB(\001)p FE(1)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p FD(x;)g(y)s(;)g FE(0)p FB(qq)23 b(\020)f FE(1)p FD(;)2821 477 y SDict begin H.S end 2821 477 a 2821 477 a SDict begin 15 H.A end 2821 477 a 2821 477 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10a) cvn /DEST pdfmark end 2821 477 a FE(\(2.10a\))212 610 y FB(@)p FD(y)k FB(P)d(t\001)p FE(1)p FD(;)14 b FE(1)p FB(u)p FD(;)31 b FB(@)p FD(x)23 b FB(P)g(t)p FD(x)975 622 y Fy(k)1010 630 y Fp(\026)1045 638 y Fq(s)1077 622 y Fx(\000)p FG(1)1165 610 y FD(;)14 b(:)g(:)g(:)g(;)g(x)1397 622 y Fy(N)1460 610 y FB(u)p FD(;)32 b Fe(Q)1620 542 y Fr(\000)1658 610 y FB(p)p FD(x;)14 b FE(1)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p FD(x;)g(y)s(;)g FE(0)p FB(qq)23 b(\020)g FE(1)p FD(;)2817 610 y SDict begin H.S end 2817 610 a 2817 610 a SDict begin 15 H.A end 2817 610 a 2817 610 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10b) cvn /DEST pdfmark end 2817 610 a FE(\(2.10b\))212 744 y FB(@)p FD(y)j FB(P)d(t\001)p FE(1)p FD(;)14 b FE(1)p FB(u)p FD(;)31 b FB(@)p FD(x)23 b FB(P)g(t)p FD(x)975 756 y Fx(\001)p Fy(k)1061 764 y Fp(\026)1096 772 y Fq(s)1132 744 y FD(;)14 b(:)g(:)g(:)g(;)g(x)1364 756 y Fy(k)1399 764 y Fp(\026)1434 772 y Fq(s)1470 744 y FB(u)p FD(;)32 b Fe(Q)1630 676 y Fr(\000)1668 744 y FB(p)p FD(x;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p FD(x;)g(y)s(;)g FE(0)p FB(qq)23 b(\020)g FE(1)p FD(;)2826 744 y SDict begin H.S end 2826 744 a 2826 744 a SDict begin 15 H.A end 2826 744 a 2826 744 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10c) cvn /DEST pdfmark end 2826 744 a FE(\(2.10c\))212 925 y FB(@)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 24 w FB(P)g(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)567 945 y Fp(\026)602 953 y Fq(s)634 937 y Fx(\000)p FG(1)722 925 y FD(;)14 b(:)g(:)g(:)g(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 12 x Fy(k)989 945 y Fp(\026)1024 953 y Fq(s)1056 937 y Fx(\001)p FG(1)1144 925 y FB(u)p FD(;)32 b Fe(Q)1304 857 y Fr(\000)1342 925 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 19 w FB(\000)18 b FD(\016)o(;)c FE(0)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray -1 w(;)g FE(0)p FD(;)g FE(0)p FB(qq)23 b(\020)f FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p FD(;)2817 925 y SDict begin H.S end 2817 925 a 2817 925 a SDict begin 15 H.A end 2817 925 a 2817 925 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10d) cvn /DEST pdfmark end 2817 925 a FE(\(2.10d\))212 1059 y FB(@)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 24 w FB(P)h(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)567 1079 y Fp(\026)602 1087 y Fq(s)634 1071 y Fx(\000)p FG(1)722 1059 y FD(;)14 b(:)g(:)g(:)g(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 12 x Fy(k)989 1079 y Fp(\026)1024 1087 y Fq(s)1056 1071 y Fx(\001)p FG(1)1144 1059 y FB(u)p FD(;)32 b Fe(Q)1304 991 y Fr(\000)1342 1059 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 19 w FB(\001)18 b FD(\016)o(;)c FE(0)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray -1 w(;)g FE(0)p FD(;)g FE(0)p FB(qq)23 b(\020)f FE(1)c FB(\001)g FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p FD(;)2826 1059 y SDict begin H.S end 2826 1059 a 2826 1059 a SDict begin 15 H.A end 2826 1059 a 2826 1059 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10e) cvn /DEST pdfmark end 2826 1059 a FE(\(2.10e\))212 1240 y Fe(Q)280 1172 y Fr(\000)318 1240 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 398 1252 a Fx(\001)p Fy(k)484 1260 y Fp(\026)519 1268 y Fq(s)551 1252 y Fx(\000)p FG(1)639 1240 y FD(;)c FE(0)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 944 1252 a Fx(\001)p Fy(k)1030 1260 y Fp(\026)1065 1268 y Fq(s)1101 1240 y FD(;)g FE(0)p FD(;)g FE(0)p FB(qq)23 b(\020)f FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p FD(;)2831 1240 y SDict begin H.S end 2831 1240 a 2831 1240 a SDict begin 15 H.A end 2831 1240 a 2831 1240 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10f) cvn /DEST pdfmark end 2831 1240 a FE(\(2.10f)6 b(\))212 1373 y Fe(Q)280 1305 y Fr(\000)318 1373 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 398 1385 a Fy(k)433 1393 y Fp(\026)468 1401 y Fq(s)500 1385 y Fx(\001)p FG(1)588 1373 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)929 1393 y Fp(\026)964 1401 y Fq(s)999 1373 y FD(;)g FE(0)p FD(;)g FE(0)p FB(qq)23 b(\020)f FE(1)c FB(\001)g FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p FD(;)2820 1373 y SDict begin H.S end 2820 1373 a 2820 1373 a SDict begin 15 H.A end 2820 1373 a 2820 1373 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10g) cvn /DEST pdfmark end 2820 1373 a FE(\(2.10g)q(\))212 1507 y Fe(Q)280 1439 y Fr(\000)318 1507 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 398 1519 a Fx(\001)p Fy(k)484 1527 y Fp(\026)519 1535 y Fq(s)551 1519 y Fx(\001)p FG(1)639 1507 y FD(;)c FB(\001)p FE(1)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1009 1519 a Fx(\001)p Fy(k)1095 1527 y Fp(\026)1130 1535 y Fq(s)1166 1507 y FD(;)g FE(0)p FD(;)g FE(0)p FB(qq)22 b(\020)h FE(1)18 b FB(\001)g FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p FD(;)2817 1507 y SDict begin H.S end 2817 1507 a 2817 1507 a SDict begin 15 H.A end 2817 1507 a 2817 1507 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10h) cvn /DEST pdfmark end 2817 1507 a FE(\(2.10h\))212 1641 y Fe(Q)280 1573 y Fr(\000)318 1641 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 398 1653 a Fy(k)433 1661 y Fp(\026)468 1669 y Fq(s)500 1653 y Fx(\000)p FG(1)588 1641 y FD(;)c FE(1)p FD(;)g FE(0)p FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)929 1661 y Fp(\026)964 1669 y Fq(s)999 1641 y FD(;)g FE(0)p FD(;)g FE(0)p FB(qq)23 b(\020)f FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2 w FB(q)p FD(;)2840 1641 y SDict begin H.S end 2840 1641 a 2840 1641 a SDict begin 15 H.A end 2840 1641 a 2840 1641 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10i) cvn /DEST pdfmark end 2840 1641 a FE(\(2.10i\))212 1774 y FB(@p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)23 b(P)g FD(E)5 b(;)32 b(v)27 b FB(\030)22 b FE(0)p FD(;)32 b Fe(Q)1062 1706 y Fr(\000)1100 1774 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 19 w FB(\000)18 b FD(\016)o(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)c(v)s FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)g(v)s FB(qq)24 b(\020)e FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p FD(;)2837 1774 y SDict begin H.S end 2837 1774 a 2837 1774 a SDict begin 15 H.A end 2837 1774 a 2837 1774 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10j) cvn /DEST pdfmark end 2837 1774 a FE(\(2.10j\))212 1908 y FB(@p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)23 b(P)g FD(E)5 b(;)32 b(v)27 b FB(\030)22 b FE(0)p FD(;)32 b Fe(Q)1062 1840 y Fr(\000)1100 1908 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 19 w FB(\001)18 b FD(\016)o(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)c(v)s FB(q)p FE(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)g(v)s FB(qq)24 b(\020)e FE(1)c FB(\001)g FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p FD(:)2819 1908 y SDict begin H.S end 2819 1908 a 2819 1908 a SDict begin 15 H.A end 2819 1908 a 2819 1908 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.10k) cvn /DEST pdfmark end 2819 1908 a FE(\(2.10k\))150 2080 y(In)28 b(Eq.)f(\()p 0 0.6 0 TeXcolorrgb 437 2080 a SDict begin H.S end 437 2080 a 0 0.6 0 TeXcolorrgb FE(2.10)p 0 0.6 0 TeXcolorrgb 586 2027 a SDict begin H.R end 586 2027 a 586 2080 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.10) cvn H.B /ANN pdfmark end 586 2080 a 0 TeXcolorgray FE(\):)0 2180 y(-)35 b(The)g(\014rst)g(three)g(lines)f FB(p)p FD(a)p FE(-)p FD(c)p FB(q)h FE(describ)r(e)f(the)i(jumps)e(of)i (the)f(mo)r(des)f(when)i(the)g(pro)r(cess)e Fh(Z)3039 2150 y Fy(\016)0 2279 y FE(reac)n(hes)26 b(the)i(b)r(oundaries)e(of)h (the)h(domain)d FB(B)s FD(E)5 b FE(:)218 2451 y SDict begin H.S end 218 2451 a 218 2451 a SDict begin 12 H.A end 218 2451 a 218 2451 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.11) cvn /DEST pdfmark end 218 2451 a FB(B)s FD(E)28 b FB(\020)22 b(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 523 2463 a Fx(\001)p Fy(k)609 2471 y Fp(\026)644 2479 y Fq(s)679 2451 y FD(;)14 b(:)g(:)g(:)g(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 12 x Fy(N)974 2451 y FB(u)19 b(\002)f(t\001)p FE(1)p FB(u)f(\002)h(t)p FE(0)p FB(u)1524 2373 y Fr(\244)1615 2451 y FB(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1700 2463 a Fx(\001)p Fy(N)1814 2451 y FD(;)c(:)g(:)g(:)f(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 2046 2463 a Fy(k)2081 2471 y Fp(\026)2116 2479 y Fq(s)2151 2451 y FB(u)19 b(\002)f(t)p FE(1)p FB(u)f(\002)h(t)p FE(0)p FB(u)p FD(:)218 b FE(\(2.11\))0 2644 y(When)22 b(the)f(pro)r(cess)f Fh(Z)725 2614 y Fy(\016)783 2644 y FE(reac)n(hes)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)1186 2644 y FD(;)14 b FB(\001)p FE(1)p FD(;)g FE(0)p FB(q)20 b FE(for)h FD(k)26 b FB(P)d(t)p FD(k)1798 2656 y Fy(\026)1838 2664 y Fq(s)1875 2644 y FB(\000)6 b FE(1)p FD(;)14 b(:)g(:)g(:)e(;)i(N)9 b FB(u)p FE(,)23 b(it)d(jumps)h(to)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2822 2656 a Fy(k)2863 2644 y FD(;)14 b FE(1)p FD(;)g FE(0)p FB(q)p FE(.)0 2744 y(When)23 b(the)g(pro)r(cess)e Fh(Z)729 2714 y Fy(\016)788 2744 y FE(reac)n(hes)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1152 2756 a Fy(k)1193 2744 y FD(;)14 b FB(\001)p FE(1)p FD(;)g FE(0)p FB(q)21 b FE(for)h FD(k)k FB(P)d(t\001)p FD(k)1872 2756 y Fy(\026)1912 2764 y Fq(s)1943 2744 y FD(;)14 b(:)g(:)g(:)g(;)g(k)2171 2756 y Fy(\026)2211 2764 y Fq(s)2242 2744 y FB(u)p FE(,)24 b(it)e(jumps)g(to)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2822 2756 a Fy(k)2863 2744 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FE(.)0 2843 y(These)25 b(jumps)g(represen)n(t)f(the)h (transitions)e(from)h(the)h(dynamic)e(phase)i(with)g(negativ)n(e)e(v)n (elo)r(cit)n(y)0 2943 y(\(mo)r(de)p 0 TeXcolorgray 34 w FD(y)p 0 TeXcolorgray 39 w FB(\020)35 b(\001)p FE(1\))f(to)h(the)g (dynamic)e(phase)i(with)f(p)r(ositiv)n(e)f(v)n(elo)r(cit)n(y)f(\(mo)r (de)p 0 TeXcolorgray 34 w FD(y)p 0 TeXcolorgray 38 w FB(\020)j FE(1\))g(and)g(to)0 3043 y(the)c(static)e(phase)h(\(mo)r(de)p 0 TeXcolorgray 30 w FD(y)p 0 TeXcolorgray 31 w FB(\020)e FE(0\).)45 b(Similarly)-7 b(,)26 b(when)31 b(the)g(pro)r(cess)e Fh(Z)2276 3013 y Fy(\016)2343 3043 y FE(reac)n(hes)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2715 3055 a Fy(k)2756 3043 y FD(;)14 b FE(1)p FD(;)g FE(0)p FB(q)30 b FE(for)0 3142 y FD(k)c FB(P)d(t\001)p FD(N)t(;)14 b(:)g(:)g(:)f(;)h FB(\001)p FD(k)601 3154 y Fy(\026)641 3162 y Fq(s)675 3142 y FB(\001)s FE(1)p FB(u)p FE(,)21 b(it)e(jumps)h(to)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)1395 3142 y FD(;)14 b FB(\001)p FE(1)p FD(;)g FE(0)p FB(q)p FE(.)33 b(When)21 b(the)f(pro)r(cess)f Fh(Z)2428 3112 y Fy(\016)2484 3142 y FE(reac)n(hes)f FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2845 3154 a Fy(k)2886 3142 y FD(;)c FE(1)p FD(;)g FE(0)p FB(q)0 3242 y FE(for)29 b FD(k)h FB(P)d(t\001)p FD(k)418 3254 y Fy(\026)458 3262 y Fq(s)489 3242 y FD(;)14 b(:)g(:)g(:)f(;)h(k)716 3254 y Fy(\026)756 3262 y Fq(s)788 3242 y FB(u)p FE(,)30 b(it)g(jumps)f(to)h FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)1437 3242 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FE(.)43 b(These)30 b(jumps)f(represen)n(t)g(the)h(transitions)0 3342 y(from)h(the)i(dynamic)d(phase)i(with)g(p)r(ositiv)n(e)e(v)n(elo)r (cit)n(y)f(\(mo)r(de)p 0 TeXcolorgray 32 w FD(y)p 0 TeXcolorgray 34 w FB(\020)h FE(1\))i(to)h(the)f(dynamic)f(phase)0 3441 y(with)c(negativ)n(e)f(v)n(elo)r(cit)n(y)e(\(mo)r(de)p 0 TeXcolorgray 27 w FD(y)p 0 TeXcolorgray 26 w FB(\020)f(\001)p FE(1\))k(and)g(to)h(the)g(static)e(phase)h(\(mo)r(de)p 0 TeXcolorgray 27 w FD(y)p 0 TeXcolorgray 26 w FB(\020)22 b FE(0\).)0 3541 y(-)27 b(The)g(follo)n(wing)c(lines)j FB(p)p FD(d)p FE(-)p FD(k)s FB(q)h FE(describ)r(e)f(the)i(jumps)f(of)g (the)g(mo)r(des)f(that)i(are)e(triggered)f(b)n(y)i(the)0 3640 y(random)j(clo)r(c)n(k)g(of)i(the)h(driving)c(noise)p 0 TeXcolorgray 30 w FD(X)1346 3610 y Fy(\016)1339 3661 y(t)p 0 TeXcolorgray 1382 3640 a FE(.)50 b(The)32 b(lines)e FB(p)p FD(d)p FE(-)p FD(g)s FB(q)i FE(describ)r(e)f(the)h(jumps)g(from) f(the)0 3740 y(static)e(phase)h(to)f(itself,)h(the)g(lines)e FB(p)p FD(h)p FE(-)p FD(i)p FB(q)i FE(describ)r(e)f(the)h(jumps)g(from) f(the)h(static)f(phase)h(to)g(the)0 3840 y(dynamic)35 b(phase)h(and)h(the)g(lines)e FB(p)p FD(j)5 b FE(-)p FD(k)s FB(q)37 b FE(describ)r(e)e(the)j(jumps)e(from)g(the)h(dynamic)e (phase)h(to)0 3939 y(itself.)e(Note)24 b(in)f(particular)e(that)j (lines)e FB(p)p FD(h)p FE(-)p FD(i)p FB(q)i FE(describ)r(e)f(ho)n(w)g (the)i(pro)r(cess)d(at)i(the)h(b)r(order)e(of)h(the)0 4039 y(static)32 b(domain)f(at)i FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 720 4051 a Fx(\010)p Fy(k)806 4059 y Fp(\026)841 4067 y Fq(s)876 4039 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)33 b FE(can)f(escap)r(e)h(the)h(static)e(domain)e(b) n(y)j(a)g(jump)g(of)p 0 TeXcolorgray 33 w FD(X)2796 4009 y Fy(\016)2789 4059 y(t)p 0 TeXcolorgray 2865 4039 a FE(whic)n(h)0 4139 y(allo)n(ws)24 b(the)k(pro)r(cess)f(to)g(pull)f (itself)g(out)i(of)f(the)h(stic)n(k)n(ed)e(phase.)150 4238 y(W)-7 b(e)30 b(denote)g FD(v)605 4250 y FG(max)759 4238 y FB(\020)d FE(inf)6 b FB(t)p FD(v)30 b FB(\245)d FE(0)p FD(;)p 0 TeXcolorgray 27 w(x)1290 4250 y Fy(N)1372 4238 y FB(\000)18 b Fs(b)p FB(p)p FD(v)s FB(q)p 0 TeXcolorgray 20 w(\001)i FD(\026)1760 4250 y FG(d)1828 4238 y FB(\244)26 b FE(0)p FB(u)p FE(.)44 b(W)-7 b(e)30 b(denote)g(b)n(y)g(\010)p 0 TeXcolorgray 12 x Fy(x)p 0 TeXcolorgray -1 w(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 2755 4238 a FB(p)p FD(t;)14 b(v)s FB(q)31 b FE(the)0 4338 y(\015o)n(w)c(solution)e(of)535 4510 y SDict begin H.S end 535 4510 a 535 4510 a SDict begin 12 H.A end 535 4510 a 535 4510 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.12) cvn /DEST pdfmark end 535 4510 a FB(B)576 4522 y Fy(t)605 4510 y FE(\010)p 0 TeXcolorgray 12 x Fy(x)p 0 TeXcolorgray -1 w(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 762 4510 a FB(p)p FD(t;)14 b(v)s FB(q)24 b(\020)e FD(B)t FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b FE(\010)p 0 TeXcolorgray 12 x Fy(x)p 0 TeXcolorgray -1 w(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 1469 4510 a FB(p)p FD(t;)g(v)s FB(qq)p FD(;)181 b FE(\010)p 0 TeXcolorgray 12 x Fy(x)p 0 TeXcolorgray(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 2036 4510 a FB(p)p FD(t)23 b FB(\020)g FE(0)p 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TeXcolorgray 14 w(y)p 0 TeXcolorgray 1090 2328 a FG(2)1127 2316 y FD(;)14 b(v)1204 2328 y FG(2)1242 2316 y FB(q)651 b FE(if)27 b FD(t)c FB(\020)g FD(T)2191 2328 y FG(2)2228 2316 y FD(:)2863 2267 y FE(\(2.16\))0 2468 y(3\))34 b(Iterate.)57 b(This)34 b(giv)n(es)e(a)i(piecewise)e(deterministic)f(tra)5 b(jectory)33 b Fh(Z)2252 2438 y Fy(\016)2246 2488 y(t)2322 2468 y FE(with)h(jump)h(times)d FD(T)3017 2480 y Fy(j)3052 2468 y FE(,)0 2568 y FD(j)c FB(\245)23 b FE(1.)150 2667 y(The)32 b(pro)r(cess)f Fh(Z)689 2637 y Fy(\016)683 2688 y(t)756 2667 y FB(\020)p 0 TeXcolorgray 30 w(p)p FD(X)959 2637 y Fy(\016)952 2688 y(t)995 2667 y FD(;)14 b(Y)1098 2637 y Fy(\016)1080 2688 y(t)1135 2667 y FD(;)g(V)1239 2637 y Fy(\016)1220 2688 y(t)1275 2667 y FB(q)p 0 TeXcolorgray 32 w FE(is)31 b(a)h(PDMP)g(as)f(in)n(tro)r(duced)g(b)n(y)g([)p 0 0 0.6 TeXcolorrgb 2454 2667 a SDict begin H.S end 2454 2667 a 0 0 0.6 TeXcolorrgb FE(10)p 0 0 0.6 TeXcolorrgb 2538 2614 a SDict begin H.R end 2538 2614 a 2538 2667 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.davis84) cvn H.B /ANN pdfmark end 2538 2667 a 0 TeXcolorgray FE(])h(and)p 0 TeXcolorgray 32 w FB(p)p FD(X)2867 2637 y Fy(\016)2860 2688 y(t)2903 2667 y FD(;)14 b(V)3006 2637 y Fy(\016)2988 2688 y(t)3043 2667 y FB(q)p 0 TeXcolorgray 0 2767 a FE(follo)n(ws)28 b(the)k(random)e(dynamics)f(\()p 0 0.6 0 TeXcolorrgb 1135 2767 a SDict begin H.S end 1135 2767 a 0 0.6 0 TeXcolorrgb FE(2.3)p 0 0.6 0 TeXcolorrgb 1242 2713 a SDict begin H.R end 1242 2713 a 1242 2767 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.3) cvn H.B /ANN pdfmark end 1242 2767 a 0 TeXcolorgray FE(-)p 0 0.6 0 TeXcolorrgb 1270 2767 a SDict begin H.S end 1270 2767 a 0 0.6 0 TeXcolorrgb FE(2.5)p 0 0.6 0 TeXcolorrgb 1377 2713 a SDict begin H.R end 1377 2713 a 1377 2767 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.5) cvn H.B /ANN pdfmark end 1377 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FB(q)30 b FE(that)f(satis\014es)e(\()p 0 0.6 0 TeXcolorrgb 2872 2958 a SDict begin H.S end 2872 2958 a 0 0.6 0 TeXcolorrgb FE(2.20)p 0 0.6 0 TeXcolorrgb 3021 2904 a SDict begin H.R end 3021 2904 a 3021 2958 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.20) cvn H.B /ANN pdfmark end 3021 2958 a 0 TeXcolorgray FE(\),)0 3057 y(w)n(e)g(ha)n(v)n(e)997 3225 y SDict begin H.S end 997 3225 a 997 3225 a SDict begin 12 H.A end 997 3225 a 997 3225 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.21) cvn /DEST pdfmark end 997 3225 a FA(E)8 b FB(r)p FD(f)h FB(p)p Fh(Z)1227 3191 y Fy(\016)1221 3245 y(t)1269 3225 y FB(q|)p Fh(Z)1394 3191 y Fy(\016)1388 3245 y FG(0)1454 3225 y FB(\020)23 b Fh(z)s FB(s)g(\020)f FD(F)12 b FB(p)p FE(0)p FD(;)i Fh(z)s FE(;)g FD(t)p FB(q)p FD(;)786 b FE(\(2.21\))0 3392 y(where)27 b FB(p)p FD(s;)14 b Fh(z)s FB(q)24 b(\336\321)f FD(F)12 b FB(p)p FD(s;)i Fh(z)s FE(;)g FD(t)p FB(q)29 b FE(is)d(the)i(solution)d(of)j(the)g(bac)n(kw)n (ard)d(Kolmogoro)n(v)d(equation)962 3560 y SDict begin H.S end 962 3560 a 962 3560 a SDict begin 12 H.A end 962 3560 a 962 3560 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.22) cvn /DEST pdfmark end 962 3560 a FB(B)1003 3572 y Fy(s)1039 3560 y FD(F)30 b FB(\000)18 b Fe(L)p FD(F)35 b FB(\020)23 b FE(0)18 b(in)f FD(E)24 b FE(for)18 b FD(s)23 b FB(P)g(p)p FE(0)p FD(;)14 b(t)p FB(q)p FD(;)750 b FE(\(2.22\))0 3728 y(with)31 b(the)h(b)r(oundary)e(condition)g(\()p 0 0.6 0 TeXcolorrgb 1118 3728 a SDict begin H.S end 1118 3728 a 0 0.6 0 TeXcolorrgb FE(2.18)p 0 0.6 0 TeXcolorrgb 1267 3674 a SDict begin H.R end 1267 3674 a 1267 3728 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.2.18) cvn H.B /ANN pdfmark end 1267 3728 a 0 TeXcolorgray FE(\))g(on)h FB(B)s FD(E)36 b FE(for)31 b FD(s)f FB(P)f(p)p FE(0)p FD(;)14 b(t)p FB(q)p FE(,)32 b(and)f(the)h(terminal)c(condition)0 3827 y FD(F)12 b FB(p)p FD(s)23 b FB(\020)g FD(t;)14 b Fh(z)s FE(;)g FD(t)p FB(q)23 b(\020)g FD(f)9 b FB(p)p Fh(z)s FB(q)p FE(.)0 3892 y SDict begin H.S end 0 3892 a 0 3892 a SDict begin 12 H.A end 0 3892 a 0 3892 a SDict begin [/View [/XYZ H.V]/Dest (section.3) cvn /DEST pdfmark end 0 3892 a 150 3971 a FJ(3.)47 b(Ergo)s(dicit)m(y)32 b(and)h(stationary)g(state.)42 b FE(Giv)n(en)27 b FD(f)37 b FE(a)28 b(function)g(in)f(the)i(domain)c(of)k Fe(L)p FE(,)0 4070 y(w)n(e)e(consider)f(the)i(function)623 4269 y SDict begin H.S end 623 4269 a 623 4269 a SDict begin 12 H.A end 623 4269 a 623 4269 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.1) cvn /DEST pdfmark end 623 4269 a FD(u)671 4281 y Fy(\025)714 4269 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FE(;)g FD(f)9 b FB(q)23 b(\020)f FA(E)1233 4284 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 5 w(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 2 w(;v)r Fx(q)1443 4176 y Fr(\021)1497 4156 y(\273)1559 4176 y Fx(8)1538 4344 y FG(0)1634 4269 y FD(e)1673 4234 y Fx(\001)p Fy(\025s)1799 4269 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)1957 4234 y Fy(\016)1950 4289 y(s)1992 4269 y FD(;)14 b(Y)2096 4234 y Fy(\016)2077 4289 y(s)2132 4269 y FD(;)g(V)2236 4234 y Fy(\016)2217 4289 y(s)p 0 TeXcolorgray 2272 4269 a FB(q)p FE(d)q FD(s)2390 4176 y Fr(\031)2429 4269 y FD(:)452 b FE(\(3.1\))0 4483 y(F)-7 b(rom)26 b(the)i(theory)f(of)h (Mark)n(o)n(v)d(pro)r(cesses)h([)p 0 0 0.6 TeXcolorrgb 1401 4483 a SDict begin H.S end 1401 4483 a 0 0 0.6 TeXcolorrgb FE(10)p 0 0 0.6 TeXcolorrgb 1485 4429 a SDict begin H.R end 1485 4429 a 1485 4483 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.davis84) cvn H.B /ANN pdfmark end 1485 4483 a 0 TeXcolorgray FE(,)p 0 0 0.6 TeXcolorrgb 1519 4483 a SDict begin H.S end 1519 4483 a 0 0 0.6 TeXcolorrgb FE(14)p 0 0 0.6 TeXcolorrgb 1603 4429 a SDict begin H.R end 1603 4429 a 1603 4483 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.MR0838085) cvn H.B /ANN pdfmark end 1603 4483 a 0 TeXcolorgray FE(],)g(it)h(satis\014es)f(the)h(equation)1137 4650 y SDict begin H.S end 1137 4650 a 1137 4650 a SDict begin 12 H.A end 1137 4650 a 1137 4650 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.2) cvn /DEST pdfmark end 1137 4650 a FD(\025u)1233 4662 y Fy(\025)1295 4650 y FB(\001)18 b Fe(L)p FD(u)1483 4662 y Fy(\025)1550 4650 y FB(\020)k FD(f)55 b FE(in)45 b FD(E)5 b(:)967 b FE(\(3.2\))0 4818 y(Let)28 b(us)f(in)n(tro)r(duce)g(the)g(stopping)g(times)p 0 TeXcolorgray 597 4985 a(^)-47 b FD(\034)628 4997 y Fy(n)697 4985 y FB(\020)23 b FE(inf)899 4917 y Fr( )943 4985 y FD(t)g FB(\245)g FD(\034)1120 4997 y Fy(n)p Fx(\001)p FG(1)1249 4985 y FD(;)p 0 TeXcolorgray 28 w(V)1367 4951 y Fy(\016)1348 5006 y(t)p 0 TeXcolorgray 1427 4985 a FB(\020)f FE(0)27 b(and)h FB(|)p 0 TeXcolorgray FD(X)1844 4951 y Fy(\016)1837 5006 y(t)p 0 TeXcolorgray 1880 4985 a FB(|)23 b(\244)f FD(\026)2063 4997 y FG(s)2094 4917 y Fr(\()2138 4985 y FD(;)96 b(n)23 b FB(\245)g FE(1)p FD(;)2904 4985 y SDict begin H.S end 2904 4985 a 2904 4985 a SDict begin 15 H.A end 2904 4985 a 2904 4985 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.3) cvn /DEST pdfmark end 2904 4985 a FE(\(3.3\))592 5123 y FD(\034)628 5135 y Fy(n)697 5123 y FB(\020)g FE(inf)899 5055 y Fr( )943 5123 y FD(t)g FB(\245)k FE(^)-46 b FD(\034)1120 5135 y Fy(n)1165 5123 y FD(;)28 b FB(p)p 0 TeXcolorgray FD(X)1324 5089 y Fy(\016)1317 5144 y(t)1360 5123 y FD(;)14 b(Y)1464 5089 y Fy(\016)1445 5144 y(t)1500 5123 y FD(;)g(V)1604 5089 y Fy(\016)1585 5144 y(t)p 0 TeXcolorgray 1640 5123 a FB(q)24 b(P)f(t)p Fs(s)1837 5135 y Fx(\001)1891 5123 y FD(;)14 b Fs(s)1965 5135 y Fx(\000)2020 5123 y FB(u)2057 5055 y Fr(\()2101 5123 y FD(;)97 b(n)23 b FB(\245)f FE(1)p FD(;)2904 5123 y SDict begin H.S end 2904 5123 a 2904 5123 a SDict begin 15 H.A end 2904 5123 a 2904 5123 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.4) cvn /DEST pdfmark end 2904 5123 a FE(\(3.4\))p 0 TeXcolorgray 0 TeXcolorgray eop end end %%Page: 10 10 TeXDict begin HPSdict begin 10 9 bop 0 TeXcolorgray 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a 0 TeXcolorgray -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.10) cvn /DEST pdfmark end -8 -8 a 0 TeXcolorgray 0 TeXcolorgray 0 83 a FE(10)965 b FI(J.)23 b(Garnier,)h(Z.)f(Lu,)h(and)g(L.)f(Mertz)p 0 TeXcolorgray 0 286 a FE(where)35 b Fs(s)285 298 y Fx(\010)375 286 y FB(\020)h(p\010)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)655 306 y Fp(\026)690 314 y Fq(s)722 298 y Fx(\000)p FG(1)810 286 y FD(;)14 b FB(\010)p FE(1)p FD(;)g FE(0)p FB(q)34 b FE(and)h FD(\034)1304 298 y FG(0)1377 286 y FB(\020)h FE(0.)p 0 TeXcolorgray 59 w(The)f(t)n(w)n(o)g(p)r(oin)n (ts)f Fs(s)2239 298 y Fx(\010)2329 286 y FE(are)g(the)i(t)n(w)n(o)e(p)r (ossible)0 386 y(exit)f(p)r(oin)n(ts)g(of)g(the)h(static)f(phase.)55 b(F)-7 b(or)33 b FD(n)g FB(\245)g FE(1,)i(the)f(stopping)e(times)37 b(^)-47 b FD(\034)2382 398 y Fy(n)2461 386 y FE(and)34 b FD(\034)2665 398 y Fy(n)2744 386 y FE(represen)n(t)0 485 y(resp)r(ectiv)n(ely)c(the)i(en)n(try)g(and)g(exit)g(times)f(of)h (the)h FD(n)p FE(-th)f(static)g(phases)f(whic)n(h)h(are)f(de\014ned)i (as)0 585 y(the)c(time)d(in)n(terv)-5 b(als)26 b(when)i FB(p)p 0 TeXcolorgray FD(X)992 555 y Fy(\016)985 605 y(t)1028 585 y FD(;)14 b(Y)1132 555 y Fy(\016)1113 605 y(t)1168 585 y FD(;)g(V)1272 555 y Fy(\016)1253 605 y(t)p 0 TeXcolorgray 1308 585 a FB(q)25 b(P)e FD(D)1503 555 y FG(0)1541 585 y FE(,)28 b FD(D)1663 555 y FG(0)1724 585 y FB(\020)c(tp)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1930 597 a Fy(k)1971 585 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FD(;)g(k)25 b FB(\020)f(\001)p FD(k)2463 597 y Fy(\026)2503 605 y Fq(s)2534 585 y FD(;)14 b(:)g(:)g(:)g(;)g(k)2762 597 y Fy(\026)2802 605 y Fq(s)2833 585 y FB(u)p FE(.)39 b(The)0 685 y(recurrence)d(and)h(ergo)r(dicit)n(y)d(of)j(the)g(Mark)n (o)n(v)e(pro)r(cess)h(is)g(a)h(consequence)f(of)i(the)f(follo)n(wing)0 784 y(prop)r(osition)25 b(\(see)i(App)r(endix)p 0 0.6 0 TeXcolorrgb 984 784 a SDict begin H.S end 984 784 a 0 0.6 0 TeXcolorrgb FE(B)p 0 0.6 0 TeXcolorrgb 1043 727 a SDict begin H.R end 1043 727 a 1043 784 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (appendix.B) cvn H.B /ANN pdfmark end 1043 784 a 0 TeXcolorgray 27 w FE(for)g(the)h(pro)r(of)6 b(\).)0 805 y SDict begin H.S end 0 805 a 0 805 a SDict begin 12 H.A end 0 805 a 0 805 a SDict begin [/View [/XYZ H.V]/Dest (thm.3.1) cvn /DEST pdfmark end 0 805 a 150 889 a Fg(Pr)n(oposition)31 b(3.1.)40 b Fz(We)30 b(have)h FA(E)1261 901 y Fb(s)1292 909 y Fd(\000)1349 821 y Fr(\020)1383 889 y FD(\034)1419 901 y FG(1)1457 821 y Fr(\030)1514 889 y FB(\240)23 b(8)p Fz(.)150 994 y FE(W)-7 b(e)39 b(prop)r(ose)f(b)r(elo)n(w)f(a)i(represen)n(tation)d(form)n(ula)g(for)i (the)i(stationary)c(measure)h(of)i(the)0 1094 y(pro)r(cess)26 b FB(p)p 0 TeXcolorgray FD(X)397 1064 y Fy(\016)390 1114 y(t)433 1094 y FD(;)14 b(Y)537 1064 y Fy(\016)518 1114 y(t)573 1094 y FD(;)g(V)677 1064 y Fy(\016)658 1114 y(t)p 0 TeXcolorgray 714 1094 a FB(q)28 b FE(that)f(is)g(based)g(on)g(the)h (functions)f FD(h)1932 1059 y Fx(\010)1932 1119 y Fy(\025)2015 1094 y FE(and)g FD(w)2235 1106 y Fy(\025)2307 1094 y FE(that)h(are)e(de\014ned)i(b)n(y)700 1296 y FD(h)748 1261 y Fx(\010)748 1321 y Fy(\025)803 1296 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)23 b(\020)g FA(E)1236 1311 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 6 w(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 1 w(;v)r Fx(q)1446 1228 y Fr(\020)1480 1296 y FD(e)1519 1262 y Fx(\001)p Fy(\025\034)1640 1270 y Fq(1)1676 1296 y FJ(1)1724 1313 y Fx(tp)p 0 TeXcolorgray Fy(X)1839 1296 y Fp(\016)1834 1329 y(\034)1862 1341 y Fq(1)1899 1313 y Fy(;Y)1972 1296 y Fp(\016)1958 1329 y(\034)1986 1341 y Fq(1)2023 1313 y Fy(;V)2096 1296 y Fp(\016)2082 1329 y(\034)2110 1341 y Fq(1)p 0 TeXcolorgray 2146 1313 a Fx(q\020)p Fb(s)2254 1321 y Fd(\010)2301 1313 y Fx(u)2335 1228 y Fr(\030)2369 1296 y FD(;)2904 1296 y SDict begin H.S end 2904 1296 a 2904 1296 a SDict begin 15 H.A end 2904 1296 a 2904 1296 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.5) cvn /DEST pdfmark end 2904 1296 a FE(\(3.5\))614 1492 y FD(w)673 1504 y Fy(\025)717 1492 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FE(;)g FD(f)9 b FB(q)23 b(\020)g FA(E)1236 1508 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 6 w(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 1 w(;v)r Fx(q)1446 1399 y Fr(\021)1500 1379 y(\273)1562 1400 y Fy(\034)1593 1408 y Fq(1)1541 1568 y FG(0)1643 1492 y FD(e)1682 1458 y Fx(\001)p Fy(\025s)1807 1492 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)1965 1458 y Fy(\016)1958 1513 y(s)2001 1492 y FD(;)14 b(Y)2105 1458 y Fy(\016)2086 1513 y(s)2141 1492 y FD(;)g(V)2245 1458 y Fy(\016)2226 1513 y(s)p 0 TeXcolorgray 2281 1492 a FB(q)p FE(d)q FD(s)2399 1399 y Fr(\031)2438 1492 y FD(;)2904 1492 y SDict begin H.S end 2904 1492 a 2904 1492 a SDict begin 15 H.A end 2904 1492 a 2904 1492 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.6) cvn /DEST pdfmark end 2904 1492 a FE(\(3.6\))0 1741 y(where)33 b FD(f)42 b FE(is)32 b(a)h(b)r(ounded)h(function.)54 b(The)33 b(functions)g FD(h)1801 1706 y Fx(\010)1801 1766 y Fy(\025)1890 1741 y FE(and)g FD(w)2116 1753 y Fy(\025)2193 1741 y FE(can)g(b)r(e)h(computed)f(as)g(ex-)0 1840 y(plained)26 b(in)g(the)i(follo)n(wing)c(prop)r(osition.)0 1857 y SDict begin H.S end 0 1857 a 0 1857 a SDict begin 12 H.A end 0 1857 a 0 1857 a SDict begin [/View [/XYZ H.V]/Dest (thm.3.2) cvn /DEST pdfmark end 0 1857 a 150 1945 a Fg(Pr)n(oposition)h(3.2.)38 b Fz(L)l(et)24 b(us)f(intr)l(o)l (duc)l(e)i(two)f(absorbing)i(states)e Fs(s)2234 1915 y Fx(1)2234 1966 y(\010)2313 1945 y Fz(and)h(a)g(mo)l(di\014e)l(d)h (kernel)0 2045 y Fe(L)57 2015 y Fx(1)109 2045 y Fz(such)k(that)220 2239 y SDict begin H.S end 220 2239 a 220 2239 a SDict begin 12 H.A end 220 2239 a 220 2239 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.7) cvn /DEST pdfmark end 220 2239 a Fe(L)277 2204 y Fx(1)300 2239 y FD(f)9 b FB(p)p Fh(z)s FB(q)24 b(\020)f FD(B)t FB(p)p Fh(z)s FB(qB)796 2251 y Fy(v)836 2239 y FD(f)9 b FB(p)p Fh(z)s FB(q)19 b(\000)p 0 TeXcolorgray 18 w FE(\003)p 0 TeXcolorgray 1269 2160 a Fr(\270)1173 2339 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 1236 2323 a Fd(1)1256 2339 y Fy(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 1312 2323 a Fd(1)1332 2339 y Fx(qP)p Ff(S)1431 2323 y Fp(\016)1458 2239 y FB(r)p FD(f)9 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray -35 x Fx(1)1638 2239 y FD(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 1719 2204 a Fx(1)1741 2239 y FD(;)14 b(v)s FB(q)19 b(\001)f FD(f)9 b FB(p)p Fh(z)s FB(qs)p Fe(Q)p FB(pp)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2327 2204 a Fx(1)2350 2239 y FD(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2430 2204 a Fx(1)2453 2239 y FD(;)14 b(v)s FB(q)p FE(;)g Fh(z)s FB(q)221 b FE(\(3.7\))0 2538 y Fz(for)31 b(al)t(l)f Fh(z)d FB(P)p 391 2471 67 4 v 23 w FD(E)5 b FB(ztp)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)695 2558 y Fp(\026)730 2566 y Fq(s)766 2538 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FD(;)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)1107 2558 y Fp(\026)1142 2566 y Fq(s)1177 2538 y FD(;)g FE(0)p FD(;)g FE(0)p FB(qu)p Fz(,)30 b Fe(L)1516 2508 y Fx(1)1538 2538 y FD(f)9 b FB(p)p Fs(s)1657 2508 y Fx(1)1657 2558 y(\010)1712 2538 y FB(q)23 b(\020)g FE(0)p Fz(,)30 b(and)209 2740 y Fe(L)266 2705 y Fx(1)289 2740 y FD(f)339 2672 y Fr(\000)377 2740 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)491 2760 y Fp(\026)526 2768 y Fq(s)562 2740 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)752 2672 y Fr(\010)812 2740 y FB(\020)p FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1010 2752 a Fy(k)1045 2760 y Fp(\026)1080 2768 y Fq(s)1116 2740 y FB(q)1148 2672 y Fr(\020)1182 2740 y FD(f)9 b FB(p)p Fs(s)1301 2705 y Fx(1)1301 2760 y(\000)1356 2740 y FB(q)19 b(\001)f FD(f)1540 2672 y Fr(\000)1577 2740 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1657 2752 a Fy(k)1692 2760 y Fp(\026)1727 2768 y Fq(s)1763 2740 y FD(;)c FE(0)p FD(;)g FE(0)p FB(q)1953 2672 y Fr(\010)o(\030)895 2873 y FB(\000)978 2805 y Fr(\000)1016 2873 y FE(1)k FB(\001)g FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1293 2885 a Fy(k)1328 2893 y Fp(\026)1363 2901 y Fq(s)1398 2873 y FB(q)1430 2805 y Fr(\010)q(\020)1503 2873 y FD(f)1553 2805 y Fr(\000)1590 2873 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1670 2885 a Fy(k)1705 2893 y Fp(\026)1740 2901 y Fq(s)1772 2885 y Fx(\001)p FG(1)1860 2873 y FD(;)c FE(0)p FD(;)g FE(0)p FB(q)2050 2805 y Fr(\010)2106 2873 y FB(\001)k FD(f)2239 2805 y Fr(\000)2276 2873 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2356 2885 a Fy(k)2391 2893 y Fp(\026)2426 2901 y Fq(s)2462 2873 y FD(;)c FE(0)p FD(;)g FE(0)p FB(q)2652 2805 y Fr(\010)o(\030)2723 2873 y FD(;)2904 2873 y SDict begin H.S end 2904 2873 a 2904 2873 a SDict begin 15 H.A end 2904 2873 a 2904 2873 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.8) cvn /DEST pdfmark end 2904 2873 a FE(\(3.8\))158 3007 y Fe(L)215 2973 y Fx(1)238 3007 y FD(f)288 2939 y Fr(\000)326 3007 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)491 3027 y Fp(\026)526 3035 y Fq(s)562 3007 y FD(;)g FE(0)p FD(;)g FE(0)p FB(q)752 2939 y Fr(\010)812 3007 y FB(\020)p FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1010 3019 a Fx(\001)p Fy(k)1096 3027 y Fp(\026)1131 3035 y Fq(s)1167 3007 y FB(q)1199 2939 y Fr(\020)1233 3007 y FD(f)1283 2939 y Fr(\000)1321 3007 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1401 3019 a Fx(\001)p Fy(k)1487 3027 y Fp(\026)1522 3035 y Fq(s)1553 3019 y Fx(\000)p FG(1)1641 3007 y FD(;)g FE(0)p FD(;)g FE(0)p FB(q)1831 2939 y Fr(\010)1887 3007 y FB(\001)k FD(f)2020 2939 y Fr(\000)2058 3007 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)2223 3027 y Fp(\026)2258 3035 y Fq(s)2294 3007 y FD(;)c FE(0)p FD(;)g FE(0)p FB(q)2484 2939 y Fr(\010)o(\030)895 3141 y FB(\000)978 3073 y Fr(\000)1016 3141 y FE(1)k FB(\001)g FD(\013)p FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1293 3153 a Fx(\001)p Fy(k)1379 3161 y Fp(\026)1414 3169 y Fq(s)1449 3141 y FB(q)1481 3073 y Fr(\010)q(\020)1554 3141 y FD(f)9 b FB(p)p Fs(s)1673 3106 y Fx(1)1673 3161 y(\001)1727 3141 y FB(q)19 b(\001)f FD(f)1911 3073 y Fr(\000)1949 3141 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2029 3153 a Fx(\001)p Fy(k)2115 3161 y Fp(\026)2150 3169 y Fq(s)2185 3141 y FD(;)c FE(0)p FD(;)g FE(0)p FB(q)2375 3073 y Fr(\010)o(\030)2447 3141 y FD(:)2904 3141 y SDict begin H.S end 2904 3141 a 2904 3141 a SDict begin 15 H.A end 2904 3141 a 2904 3141 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.9) cvn /DEST pdfmark end 2904 3141 a FE(\(3.9\))0 3343 y Fz(The)31 b(functions)e FD(h)578 3308 y Fx(\010)578 3368 y Fy(\025)663 3343 y Fz(and)h FD(w)883 3355 y Fy(\025)927 3343 y FB(p\004)p FE(;)14 b FD(f)9 b FB(q)30 b Fz(de\014ne)l(d)g(by)g(\()p 0 0.6 0 TeXcolorrgb 1553 3343 a SDict begin H.S end 1553 3343 a 0 0.6 0 TeXcolorrgb Fz(3.5)p 0 0.6 0 TeXcolorrgb 1662 3290 a SDict begin H.R end 1662 3290 a 1662 3343 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.5) cvn H.B /ANN pdfmark end 1662 3343 a 0 TeXcolorgray Fz(\))h(and)f(\()p 0 0.6 0 TeXcolorrgb 1922 3343 a SDict begin H.S end 1922 3343 a 0 0.6 0 TeXcolorrgb Fz(3.6)p 0 0.6 0 TeXcolorrgb 2031 3290 a SDict begin H.R end 2031 3290 a 2031 3343 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.6) cvn H.B /ANN pdfmark end 2031 3343 a 0 TeXcolorgray Fz(\))h(satisfy)572 3537 y FD(\025h)668 3502 y Fx(\000)668 3562 y Fy(\025)742 3537 y FB(\001)18 b Fe(L)882 3502 y Fx(1)905 3537 y FD(h)953 3502 y Fx(\000)953 3562 y Fy(\025)1031 3537 y FB(\020)23 b FE(0)47 b Fz(in)h FD(E)5 b(;)184 b(h)1649 3502 y Fx(\000)1649 3562 y Fy(\025)1704 3537 y FB(p)p Fs(s)1773 3502 y Fx(1)1773 3557 y(\000)1828 3537 y FB(q)24 b(\020)e FE(1)p FD(;)32 b(h)2116 3502 y Fx(\000)2116 3562 y Fy(\025)2171 3537 y FB(p)p Fs(s)2240 3502 y Fx(1)2240 3557 y(\001)2295 3537 y FB(q)23 b(\020)g FE(0)p FD(;)2863 3537 y SDict begin H.S end 2863 3537 a 2863 3537 a SDict begin 15 H.A end 2863 3537 a 2863 3537 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.10) cvn /DEST pdfmark end 2863 3537 a FE(\(3.10\))572 3670 y FD(\025h)668 3635 y Fx(\001)668 3695 y Fy(\025)742 3670 y FB(\001)18 b Fe(L)882 3636 y Fx(1)905 3670 y FD(h)953 3635 y Fx(\001)953 3695 y Fy(\025)1031 3670 y FB(\020)23 b FE(0)47 b Fz(in)h FD(E)5 b(;)184 b(h)1649 3635 y Fx(\001)1649 3695 y Fy(\025)1704 3670 y FB(p)p Fs(s)1773 3636 y Fx(1)1773 3691 y(\000)1828 3670 y FB(q)24 b(\020)e FE(0)p FD(;)32 b(h)2116 3635 y Fx(\001)2116 3695 y Fy(\025)2171 3670 y FB(p)p Fs(s)2240 3636 y Fx(1)2240 3691 y(\001)2295 3670 y FB(q)23 b(\020)g FE(1)p FD(;)2863 3670 y SDict begin H.S end 2863 3670 a 2863 3670 a SDict begin 15 H.A end 2863 3670 a 2863 3670 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.11) cvn /DEST pdfmark end 2863 3670 a FE(\(3.11\))0 3864 y Fz(and)584 4057 y SDict begin H.S end 584 4057 a 584 4057 a SDict begin 12 H.A end 584 4057 a 584 4057 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.12) cvn /DEST pdfmark end 584 4057 a FD(\025w)691 4069 y Fy(\025)736 4057 y FB(p\004)p FE(;)14 b FD(f)9 b FB(q)18 b(\001)g Fe(L)1068 4023 y Fx(1)1091 4057 y FD(w)1150 4069 y Fy(\025)1194 4057 y FB(p\004)p FE(;)c FD(f)9 b FB(q)23 b(\020)g FD(f)57 b Fz(in)48 b FD(E)5 b(;)184 b(w)2029 4069 y Fy(\025)2072 4057 y FB(p)p Fs(s)2141 4023 y Fx(1)2141 4078 y(\010)2197 4057 y FE(;)14 b FD(f)9 b FB(q)22 b(\020)h FE(0)p FD(:)372 b FE(\(3.12\))150 4356 y Fz(Pr)l(o)l(of)p FE(.)42 b(A)29 b(tra)5 b(jectory)27 b(of)p 0 TeXcolorgray 28 w FB(p)p FD(X)1090 4326 y Fy(\016)1126 4356 y FD(;)14 b(Y)1230 4326 y Fy(\016)1266 4356 y FD(;)g(V)1370 4326 y Fy(\016)1407 4356 y FB(q)p 0 TeXcolorgray 29 w FE(can)28 b(reac)n(h)f Fs(s)1878 4368 y Fx(\000)1962 4356 y FE(b)n(y)i(di\013eren)n(t)e(w)n(a) n(ys.)39 b(Indeed,)29 b(just)0 4456 y(b)r(efore)20 b(the)h(time)e(at)h (whic)n(h)f Fs(s)921 4468 y Fx(\000)997 4456 y FE(is)g(reac)n(hed,)h (the)h(pro)r(cess)e(can)h(b)r(e)h(in)f(a)g(static)f(phase)h(at)g(the)h (p)r(oin)n(t)0 4555 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 80 4567 a Fy(k)115 4575 y Fp(\026)150 4583 y Fq(s)186 4555 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)22 b FE(\(and)h(it)g(jumps)g(from)f(the)h(static)f(phase)h(to)g(the)h (dynamic)d(phase\))i(or)f(else)g(it)h(can)g(b)r(e)0 4655 y(in)k(a)h(dynamic)d(phase)j(at)g FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)949 4675 y Fp(\026)984 4683 y Fq(s)1016 4667 y Fx(\000)p FG(1)1104 4655 y FD(;)14 b FB(\001)p FE(1)p FD(;)g(v)s FB(q)p FE(,)28 b FD(v)f FB(\240)c FE(0,)k(and)h(it)f(jumps)h(to)g Fs(s)2290 4667 y Fx(\000)2373 4655 y FE(when)p 0 TeXcolorgray 28 w FD(V)p 0 TeXcolorgray 2657 4625 a Fy(\016)2657 4675 y(t)2721 4655 y FE(reac)n(hes)e(0.)0 4755 y(This)20 b(commen)n(t)f(motiv)-5 b(ates)19 b(the)j(in)n(tro)r(duction)c(of)j(the)h(t)n(w)n(o)e (absorbing)f(states)h Fs(s)2523 4724 y Fx(1)2523 4775 y(\010)2578 4755 y FE(.)35 b(The)21 b(Mark)n(o)n(v)0 4854 y(pro)r(cess)p 0 TeXcolorgray 24 w FB(p)p FD(X)395 4824 y Fy(\016)o(;)p Fx(1)465 4854 y FD(;)14 b(Y)569 4824 y Fy(\016)o(;)p Fx(1)640 4854 y FD(;)g(V)743 4824 y Fy(\016)o(;)p Fx(1)814 4854 y FB(q)p 0 TeXcolorgray 25 w FE(with)25 b(the)g(mo)r(di\014ed)e(k)n(ernel)g Fe(L)1833 4824 y Fx(1)1881 4854 y FE(follo)n(ws)f(the)j(same)e(dynamics)g(as)h (the)0 4954 y(original)i(pro)r(cess)p 0 TeXcolorgray 30 w FB(p)p FD(X)704 4924 y Fy(\016)740 4954 y FD(;)14 b(Y)844 4924 y Fy(\016)880 4954 y FD(;)g(V)984 4924 y Fy(\016)1020 4954 y FB(q)p 0 TeXcolorgray FE(,)32 b(except)f(for)f(one) h(asp)r(ect:)43 b(when)31 b(the)g(original)c(pro)r(cess)i(is)h(at)0 5053 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 80 5065 a Fy(k)115 5073 y Fp(\026)150 5081 y Fq(s)186 5053 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)32 b FE(\(resp.)52 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 744 5065 a Fx(\001)p Fy(k)830 5073 y Fp(\026)865 5081 y Fq(s)901 5053 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FE(\))32 b(and)h(jumps)f(to)h(the)h(east)e(\(resp.)53 b(to)32 b(the)i(w)n(est\),)g(it)e(jumps)0 5153 y(to)c Fs(s)139 5165 y Fx(\000)221 5153 y FE(\(resp.)37 b Fs(s)499 5165 y Fx(\001)554 5153 y FE(\);)29 b(when)f(the)g(mo)r(di\014ed)e(pro)r (cess)h(is)f(at)i FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1892 5165 a Fy(k)1927 5173 y Fp(\026)1962 5181 y Fq(s)1997 5153 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)27 b FE(\(resp.)38 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)2621 5173 y Fp(\026)2656 5181 y Fq(s)2692 5153 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FE(\))27 b(and)p 0 TeXcolorgray 0 TeXcolorgray eop end end %%Page: 11 11 TeXDict begin HPSdict begin 11 10 bop 0 TeXcolorgray 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a 0 TeXcolorgray -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.11) cvn /DEST pdfmark end -8 -8 a 0 TeXcolorgray 0 TeXcolorgray 1050 83 a FI(Dry)23 b(friction)i(problem)f(with)h(noise)968 b FE(11)p 0 TeXcolorgray 0 286 a(jumps)30 b(to)g(the)h(east)f(\(resp.) 44 b(to)31 b(the)f(w)n(est\),)h(it)f(jumps)g(to)g Fs(s)1895 256 y Fx(1)1895 307 y(\000)1980 286 y FE(\(resp.)45 b Fs(s)2266 256 y Fx(1)2266 307 y(\001)2321 286 y FE(\))31 b(and)f(do)r(es)g(not)g(mo)n(v)n(e)0 386 y(an)n(ymore.)k(As)28 b(a)f(consequence,)g(w)n(e)g(ha)n(v)n(e)f(for)h(an)n(y)g FB(p)p 0 TeXcolorgray FD(x;)14 b(y)p 0 TeXcolorgray 4 w(;)g(v)s FB(q)23 b(P)g FD(E)5 b FE(:)649 560 y FD(h)697 525 y 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[/XYZ H.V]/Dest (equation.3.13) cvn /DEST pdfmark end 2863 560 a FE(\(3.13\))562 812 y FD(w)621 824 y Fy(\025)665 812 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FE(;)g FD(f)9 b FB(q)23 b(\020)g FA(E)1184 827 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 6 w(;)p 0 TeXcolorgray(y)p 0 TeXcolorgray 1 w(;v)r Fx(q)1394 719 y Fr(\021)1448 699 y(\273)1510 719 y Fy(\034)1548 694 y Fd(1)1541 736 y Fq(1)1489 887 y FG(0)1591 812 y FD(e)1630 777 y Fx(\001)p Fy(\025s)1756 812 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1913 777 a Fy(\016)o(;)p Fx(1)1913 832 y Fy(s)1984 812 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 2087 777 a Fy(\016)o(;)p Fx(1)2087 832 y Fy(s)2158 812 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 2262 777 a Fy(\016)o(;)p Fx(1)2262 832 y Fy(s)2333 812 y FB(q)p FE(d)p FD(s)2450 719 y Fr(\031)2490 812 y FD(;)2863 812 y SDict begin H.S end 2863 812 a 2863 812 a SDict begin 15 H.A end 2863 812 a 2863 812 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.14) cvn /DEST pdfmark end 2863 812 a FE(\(3.14\))0 1015 y(where)751 1177 y FD(\034)796 1143 y Fx(1)787 1198 y FG(1)848 1177 y FB(\020)22 b FE(inf)1050 1109 y Fr( )1094 1177 y FD(t)h FB(\245)g FE(0)p FD(;)14 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1421 1137 a Fy(\016)o(;)p Fx(1)1421 1198 y Fy(t)1491 1177 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 1595 1137 a Fy(\016)o(;)p Fx(1)1595 1198 y Fy(t)1666 1177 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1770 1137 a Fy(\016)o(;)p Fx(1)1770 1198 y Fy(t)1841 1177 y FB(q)23 b(P)g(t)p Fs(s)2037 1143 y Fx(1)2037 1198 y(\001)2092 1177 y FD(;)14 b Fs(s)2166 1143 y Fx(1)2166 1198 y(\000)2220 1177 y FB(u)2257 1109 y Fr(\()2301 1177 y FD(;)0 1339 y FE(and)27 b(the)h(statemen)n(t)f(of)h(the)g(prop)r (osition)c(follo)n(ws)h(immediately)-7 b(.)p 2135 1287 39 5 v 2135 1334 5 47 v 2168 1334 V 2135 1339 39 5 v 150 1439 a(The)22 b(function)f FD(w)693 1451 y Fy(\025)737 1439 y FB(p\004)p FE(;)14 b(1)p FB(q)21 b FE(is)g FD(w)1061 1451 y Fy(\025)1105 1439 y FB(p\004)p FE(;)14 b FD(f)9 b FB(q)22 b FE(when)f FD(f)32 b FB(\020)23 b FE(1.)34 b(The)22 b(follo)n(wing)17 b(prop)r(osition)i(is)h(inspired)0 1538 y(from)26 b([)p 0 0 0.6 TeXcolorrgb 219 1538 a SDict begin H.S end 219 1538 a 0 0 0.6 TeXcolorrgb FE(6)p 0 0 0.6 TeXcolorrgb 261 1485 a SDict begin H.R end 261 1485 a 261 1538 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (cite.MR2922084) cvn H.B /ANN pdfmark end 261 1538 a 0 TeXcolorgray FE(])i(and)f(is)f(pro)n(v)n(ed)h(in)f(App)r(endix)p 0 0.6 0 TeXcolorrgb 1304 1538 a SDict begin H.S end 1304 1538 a 0 0.6 0 TeXcolorrgb FE(C)p 0 0.6 0 TeXcolorrgb 1364 1481 a SDict begin H.R end 1364 1481 a 1364 1538 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (appendix.C) cvn H.B /ANN pdfmark end 1364 1538 a 0 TeXcolorgray FE(.)1387 1538 y SDict begin H.S end 1387 1538 a 1387 1538 a SDict begin 12 H.A end 1387 1538 a 1387 1538 a SDict begin [/View [/XYZ H.V]/Dest (thm.3.3) cvn /DEST pdfmark end 1387 1538 a 150 1638 a Fg(Pr)n(oposition)31 b(3.3.)40 b Fz(We)30 b(have)h(the)e(r)l(epr)l(esentation)h(formula)475 1800 y FD(u)523 1812 y Fy(\025)566 1800 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FE(;)g FD(f)9 b FB(q)23 b(\020)p FD(w)1072 1812 y Fy(\025)1116 1800 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FE(;)g FD(f)9 b FB(q)18 b(\001)g FD(\031)1623 1812 y Fy(\025)1667 1800 y FB(p)p FD(f)9 b FB(q)p FD(w)1840 1812 y Fy(\025)1884 1800 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FE(;)g(1)p FB(q)1031 1981 y(\000)k FD(\026)1164 1993 y Fy(\025)1208 1981 y FB(p)p FD(f)9 b FB(q)1322 1913 y Fr(\000)1360 1981 y FD(h)1408 1946 y Fx(\000)1408 2006 y Fy(\025)1463 1981 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)19 b(\001)f FD(h)1885 1946 y Fx(\001)1885 2006 y Fy(\025)1940 1981 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)c(v)s FB(q)2212 1913 y Fr(\010)2269 1981 y FB(\000)2362 1925 y FD(\031)2409 1937 y Fy(\025)2453 1925 y FB(p)p FD(f)9 b FB(q)p 2362 1962 205 4 v 2440 2038 a FD(\025)2577 1981 y(;)2863 1981 y SDict begin H.S end 2863 1981 a 2863 1981 a SDict begin 15 H.A end 2863 1981 a 2863 1981 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.15) cvn /DEST pdfmark end 2863 1981 a FE(\(3.15\))0 2171 y Fz(for)31 b(al)t(l)f FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)23 b(P)g FD(E)5 b Fz(,)30 b(wher)l(e)138 2380 y SDict begin H.S end 138 2380 a 138 2380 a SDict begin 12 H.A end 138 2380 a 138 2380 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.16) cvn /DEST pdfmark end 138 2380 a FD(\031)185 2392 y Fy(\025)229 2380 y FB(p)p FD(f)9 b FB(q)23 b(\020)463 2324 y FD(w)522 2336 y Fy(\025)566 2324 y FB(p)p Fs(s)635 2336 y Fx(\000)691 2324 y FE(;)14 b FD(f)9 b FB(q)18 b(\000)g FD(w)970 2336 y Fy(\025)1014 2324 y FB(p)p Fs(s)1083 2336 y Fx(\001)1138 2324 y FE(;)c FD(f)9 b FB(q)p 463 2361 794 4 v 670 2437 a FE(2)p FD(w)771 2449 y Fy(\025)815 2437 y FB(p)p Fs(s)884 2449 y Fx(\000)939 2437 y FE(;)14 b(1)p FB(q)1315 2380 y Fz(and)48 b FD(\026)1544 2392 y Fy(\025)1588 2380 y FB(p)p FD(f)9 b FB(q)23 b(\020)1861 2324 y FD(w)1920 2336 y Fy(\025)1964 2324 y FB(p)p Fs(s)2033 2336 y Fx(\000)2088 2324 y FE(;)14 b FD(f)9 b FB(q)18 b(\001)g FD(w)2367 2336 y Fy(\025)2411 2324 y FB(p)p Fs(s)2480 2336 y Fx(\001)2535 2324 y FE(;)c FD(f)9 b FB(q)p 1823 2361 870 4 v 1823 2442 a FE(2)p FB(p)p FE(1)18 b FB(\001)g FD(h)2088 2407 y Fx(\000)2088 2467 y Fy(\025)2142 2442 y FB(p)p Fs(s)2211 2454 y Fx(\000)2267 2442 y FB(q)g(\000)g FD(h)2448 2407 y Fx(\001)2448 2467 y Fy(\025)2503 2442 y FB(p)p Fs(s)2572 2454 y Fx(\000)2627 2442 y FB(qq)2702 2380 y FD(:)138 b FE(\(3.16\))0 2595 y Fz(We)33 b(have)i(the)e(fol)t (lowing)j(char)l(acterization)f(for)g(the)e(stationary)h(distribution)g (of)g(the)g(pr)l(o)l(c)l(ess)0 2695 y FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 108 2664 a Fy(\016)108 2715 y(t)144 2695 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 248 2664 a Fy(\016)248 2715 y(t)284 2695 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 388 2664 a Fy(\016)388 2715 y(t)424 2695 y FB(q)p Fz(:)608 2904 y SDict begin H.S end 608 2904 a 608 2904 a SDict begin 12 H.A end 608 2904 a 608 2904 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.17) cvn /DEST pdfmark end 608 2904 a FD(\031)s FB(p)p FD(f)9 b FB(q)23 b(\020)34 b FE(lim)883 2958 y Fy(\025)p Fx(\321)p FG(0)1034 2904 y FD(\025u)1130 2916 y Fy(\025)1174 2904 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FE(;)g FD(f)9 b FB(q)23 b(\020)1654 2848 y FD(w)1713 2860 y FG(0)1750 2848 y FB(p)p Fs(s)1819 2860 y Fx(\000)1874 2848 y FE(;)14 b FD(f)9 b FB(q)19 b(\000)f FD(w)2154 2860 y FG(0)2191 2848 y FB(p)p Fs(s)2260 2860 y Fx(\001)2316 2848 y FE(;)c FD(f)9 b FB(q)p 1654 2885 781 4 v 1857 2961 a FE(2)p FD(w)1958 2973 y FG(0)1996 2961 y FB(p)p Fs(s)2065 2973 y Fx(\000)2120 2961 y FE(;)14 b(1)p FB(q)2444 2904 y FD(;)396 b FE(\(3.17\))0 3110 y Fz(for)31 b(any)f(b)l(ounde)l(d) g(function)g FD(f)9 b Fz(.)0 3169 y SDict begin H.S end 0 3169 a 0 3169 a SDict begin 12 H.A end 0 3169 a 0 3169 a SDict begin [/View [/XYZ H.V]/Dest (section.4) cvn /DEST pdfmark end 0 3169 a 150 3253 a FJ(4.)47 b(Dynamical)31 b(prop)s(erties.)0 3312 y SDict begin H.S end 0 3312 a 0 3312 a SDict begin 12 H.A end 0 3312 a 0 3312 a SDict begin [/View [/XYZ H.V]/Dest (subsection.4.1) cvn /DEST pdfmark end 0 3312 a 150 3395 a FJ(4.1.)46 b(Excursions.)41 b FE(The)24 b(random)d(v)-5 b(ariables)21 b FB(p)p FD(\034)1741 3407 y Fy(n)p Fx(\000)p FG(1)1881 3395 y FB(\001)11 b FD(\034)1993 3407 y Fy(n)2038 3395 y FB(q)2070 3407 y Fy(n)p Fx(\245)p FG(0)2224 3395 y FE(are)22 b(in)n(tegrable,)g(indep)r (en-)0 3495 y(den)n(t)k(and)g(iden)n(tically)c(distributed.)35 b(This)25 b(follo)n(ws)f(from)g(the)j(strong)e(Mark)n(o)n(v)f(prop)r (ert)n(y)-7 b(,)25 b(from)0 3594 y(the)32 b(fact)g(that)g FD(\034)535 3606 y FG(1)604 3594 y FE(is)f(in)n(tegrable)d(under)k FA(P)1373 3606 y Fb(s)1404 3614 y Fd(\000)1485 3594 y FE(\(w)n(e)g(ha)n(v)n(e)f FD(\034)1876 3606 y FG(0)1943 3594 y FB(\020)e FE(0)j(a.s.)48 b(under)32 b FA(P)2572 3606 y Fb(s)2603 3614 y Fd(\000)2653 3594 y FE(\),)h(and)e(from)0 3694 y(the)f(symmetry)e(of)h(the)i(system)d(whic)n(h)h(implies)d(that)k (the)g(distributions)d(of)j FD(\034)2527 3706 y FG(1)2594 3694 y FE(starting)e(from)0 3794 y Fs(s)37 3806 y Fx(\000)120 3794 y FE(and)f(from)f Fs(s)514 3806 y Fx(\001)597 3794 y FE(are)g(iden)n(tical.)150 3893 y(F)-7 b(or)36 b(an)n(y)g(b)r(ounded) h(\(in)g(fact,)i FD(\031)s FE(-in)n(tegrable\))34 b(function)i FD(f)9 b FE(,)39 b FD(\031)s FB(p)p FD(f)9 b FB(q)38 b FE(can)e(b)r(e)h(computed)f(b)n(y)0 3993 y(\()p 0 0.6 0 TeXcolorrgb 32 3993 a SDict begin H.S end 32 3993 a 0 0.6 0 TeXcolorrgb FE(3.17)p 0 0.6 0 TeXcolorrgb 181 3939 a SDict begin H.R end 181 3939 a 181 3993 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.17) cvn H.B /ANN pdfmark end 181 3993 a 0 TeXcolorgray FE(\).)g(By)27 b(ergo)r(dicit)n(y)e(w)n(e)i (also)f(ha)n(v)n(e)700 4202 y SDict begin H.S end 700 4202 a 700 4202 a SDict begin 12 H.A end 700 4202 a 700 4202 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.1) cvn /DEST pdfmark end 700 4202 a FD(\031)s FB(p)p FD(f)9 b FB(q)23 b(\020)1098 4145 y FE(1)p 985 4182 269 4 v 985 4259 a FA(E)1034 4271 y Fb(s)1065 4279 y Fd(\000)1122 4259 y FB(r)p FD(\034)1187 4271 y FG(1)1225 4259 y FB(s)1263 4202 y FA(E)1312 4214 y Fb(s)1344 4222 y Fd(\000)1401 4109 y Fr(\021)1454 4089 y(\273)1516 4109 y Fy(\034)1547 4117 y Fq(1)1496 4277 y FG(0)1597 4202 y FD(f)1638 4214 y FG(ev)n(en)1771 4202 y FB(p)p 0 TeXcolorgray FD(X)1879 4167 y Fy(\016)1872 4222 y(s)1915 4202 y FD(;)14 b(Y)2019 4167 y Fy(\016)2000 4222 y(s)2055 4202 y FD(;)g(V)2159 4167 y Fy(\016)2140 4222 y(s)p 0 TeXcolorgray 2195 4202 a FB(q)p FE(d)q FD(s)2313 4109 y Fr(\031)2352 4202 y FD(;)529 b FE(\(4.1\))0 4419 y(with)39 b FD(f)242 4431 y FG(ev)n(en)374 4419 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)43 b(\020)f(p)p FD(f)9 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)27 b(\000)f FD(f)9 b FB(p\001)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray -1 w(;)14 b FB(\001)p 0 TeXcolorgray FD(y)p 0 TeXcolorgray 3 w(;)g FB(\001)p FD(v)s FB(qq{)p FE(2.)71 b(Indeed,)42 b(on)d(the)h(one)f(hand,)j(b)n(y)0 4519 y(symmetry)33 b(of)i(the)g(system)f FB(p\001)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1103 4489 a Fy(\016)1103 4539 y(t)1140 4519 y FD(;)14 b FB(\001)p 0 TeXcolorgray FD(Y)p 0 TeXcolorgray 1308 4489 a Fy(\016)1308 4539 y(t)1344 4519 y FD(;)g FB(\001)p 0 TeXcolorgray FD(V)p 0 TeXcolorgray 1512 4489 a Fy(\016)1512 4539 y(t)1549 4519 y FB(q)35 b FE(has)g(the)g(same)f (stationary)f(distribution)f(as)0 4618 y FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 108 4588 a Fy(\016)108 4639 y(t)144 4618 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 248 4588 a Fy(\016)248 4639 y(t)284 4618 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 388 4588 a Fy(\016)388 4639 y(t)424 4618 y FB(q)p FE(.)66 b(Therefore,)38 b(if)f FD(f)46 b FE(is)36 b(o)r(dd,)j(then)f FD(\031)s FB(p)p FD(f)9 b FB(q)39 b(\020)g FE(0)d([this)h(follo)n(ws)d(also)h(from)h(\()p 0 0.6 0 TeXcolorrgb 2895 4618 a SDict begin H.S end 2895 4618 a 0 0.6 0 TeXcolorrgb FE(3.17)p 0 0.6 0 TeXcolorrgb 3044 4565 a SDict begin H.R end 3044 4565 a 3044 4618 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.17) cvn H.B /ANN pdfmark end 3044 4618 a 0 TeXcolorgray FE(\))0 4718 y(since)28 b FD(w)264 4730 y FG(0)301 4718 y FB(p)p Fs(s)370 4730 y Fx(\001)425 4718 y FD(;)14 b(f)9 b FB(q)25 b(\020)g FD(w)718 4730 y FG(0)755 4718 y FB(p)p Fs(s)824 4730 y Fx(\000)879 4718 y FD(;)14 b(f)9 b FB(p\001\004qq)25 b(\020)g FD(w)1324 4730 y FG(0)1362 4718 y FB(p)p Fs(s)1431 4730 y Fx(\000)1486 4718 y FD(;)14 b FB(\001)p FD(f)9 b FB(q)24 b(\020)h(\001)p FD(w)1908 4730 y FG(0)1945 4718 y FB(p)p Fs(s)2014 4730 y Fx(\000)2069 4718 y FD(;)14 b(f)9 b FB(q)29 b FE(when)g FD(f)37 b FE(is)28 b(o)r(dd].)40 b(On)29 b(the)0 4818 y(other)k(hand,)j(denoting)d FD(")849 4830 y Fy(n)927 4818 y FB(\020)h FE(sgn)o FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1254 4788 a Fy(\016)1254 4838 y(\034)1285 4846 y Fp(n)1329 4818 y FB(q)p FE(,)i(the)f(strong)d(Mark)n(o)n(v)g (prop)r(ert)n(y)h(implies)d(that)35 b(the)0 4917 y(excursions)30 b FB(p)p FD(")476 4929 y Fy(n)p 0 TeXcolorgray 521 4917 a FD(X)p 0 TeXcolorgray 596 4887 a Fy(\016)596 4938 y(\034)627 4946 y Fp(n)667 4938 y Fx(\000)p Fy(t)748 4917 y FD(;)14 b(")824 4929 y 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y(t)p 0 TeXcolorgray 2569 1820 a FD(V)p 0 TeXcolorgray 2636 1790 a Fy(\016)2636 1840 y FG(0)2673 1820 y FB(s)14 b FE(cos)o FB(p)p FD(!)s(t)p FB(q)p FE(d)p FD(t)p FE(.)0 1940 y(Using)j(Leb)r(esgue's)h(dominated)e (con)n(v)n(ergence)g(theorem)h(and)h(the)h(in)n(tegrabilit)n(y)13 b(of)18 b FD(t)23 b FB(\336\321)g FA(E)2834 1952 y Fy(\031)2885 1940 y FB(r)p 0 TeXcolorgray FD(V)p 0 TeXcolorgray 2980 1910 a Fy(\016)2980 1961 y(t)p 0 TeXcolorgray 3017 1940 a FD(V)p 0 TeXcolorgray 3084 1910 a Fy(\016)3084 1961 y FG(0)3121 1940 y FB(s)0 2040 y FE(\(see)28 b(App)r(endix)p 0 0.6 0 TeXcolorrgb 547 2040 a SDict begin H.S end 547 2040 a 0 0.6 0 TeXcolorrgb FE(D)p 0 0.6 0 TeXcolorrgb 610 1983 a SDict begin H.R end 610 1983 a 610 2040 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (appendix.D) cvn H.B /ANN pdfmark end 610 2040 a 0 TeXcolorgray FE(\),)g(w)n(e)g(get)588 2260 y(lim)534 2313 y Fy(T)9 b Fx(\321\0008)789 2204 y FE(1)p 780 2241 61 4 v 780 2317 a FD(T)850 2260 y(S)901 2272 y Fy(v)r(;T)1008 2260 y FB(p)p FD(!)s FB(q)23 b(\020)g FD(S)1289 2272 y Fy(v)1328 2260 y FB(p)p FD(!)s FB(q)h(\020)e FE(2)1614 2147 y Fr(\273)1676 2167 y Fx(\0008)1655 2335 y FG(0)1802 2260 y FA(E)1852 2272 y Fy(\031)1903 2260 y FB(r)p 0 TeXcolorgray FD(V)p 0 TeXcolorgray 1998 2226 a Fy(\016)1998 2280 y FG(0)p 0 TeXcolorgray 2035 2260 a FD(V)p 0 TeXcolorgray 2102 2226 a Fy(\016)2102 2280 y(t)2139 2260 y FB(s)14 b FE(cos)n FB(p)p FD(!)s(t)p FB(q)p FE(d)q FD(t:)0 2477 y FE(W)-7 b(e)19 b(can)f(write)f FA(E)529 2489 y Fy(\031)580 2477 y FB(r)p 0 TeXcolorgray FD(V)p 0 TeXcolorgray 676 2447 a Fy(\016)676 2498 y FG(0)p 0 TeXcolorgray 713 2477 a FD(V)p 0 TeXcolorgray 780 2447 a Fy(\016)780 2498 y(t)816 2477 y FB(s)23 b(\020)g FA(E)1005 2489 y Fy(\031)1056 2477 y FB(r)p 0 TeXcolorgray FD(V)p 0 TeXcolorgray 1151 2447 a Fy(\016)1151 2498 y FG(0)1189 2477 y FA(E)8 b FB(r)p 0 TeXcolorgray FD(V)p 0 TeXcolorgray 1340 2447 a Fy(\016)1340 2498 y(t)1376 2477 y FB(|)p 0 TeXcolorgray 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FB(\020)p 0 TeXcolorgray 22 w FD(y)p 0 TeXcolorgray 3 w(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 880 2547 a Fy(\016)880 2597 y FG(0)940 2577 y FB(\020)23 b FD(v)s FB(s)k FE(is)g(the)h(solution)d(of)625 2739 y FB(pB)698 2751 y Fy(t)745 2739 y FB(\001)18 b Fe(L)p FB(q)p FD(\036)24 b FB(\020)f FE(0)18 b(in)g FD(E)5 b(;)32 b(t)23 b FB(\241)g FE(0)p FD(;)179 b(\036)p FB(p)p FD(t)24 b FB(\020)e FE(0)p FD(;)14 b(v)s(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray FB(q)23 b(\020)g FD(v)s(:)0 2911 y FE(The)28 b(function)507 2889 y(^)496 2911 y FD(\036)p FB(p)p FD(!)s(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)24 b(\020)1020 2844 y Fr(\263)1055 2864 y Fx(8)1053 2940 y FG(0)1130 2911 y FD(\036)p FB(p)p FD(t;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)g FE(exp)p FB(p\001)p Fh(i)p FD(!)s(t)p FB(q)p FE(d)o FD(t)28 b FE(satis\014es)e(\()p 0 0.6 0 TeXcolorrgb 2349 2911 a SDict begin H.S end 2349 2911 a 0 0.6 0 TeXcolorrgb FE(4.4)p 0 0.6 0 TeXcolorrgb 2456 2857 a SDict begin H.R end 2456 2857 a 2456 2911 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.4.4) cvn H.B /ANN pdfmark end 2456 2911 a 0 TeXcolorgray FE(\))h(b)r(ecause)0 2963 y Fr(\263)35 2984 y Fx(\0008)32 3060 y FG(0)161 3030 y FB(B)202 3042 y Fy(t)231 3030 y FD(\036)p FB(p)p FD(t;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)g FE(exp)p FB(p\001)p Fh(i)p FD(!)s(t)p FB(q)p FE(d)p FD(t)23 b FB(\020)g(\001)p FD(\036)p FB(p)p FD(t)g FB(\020)g FE(0)p FD(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray -1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)14 b(v)s FB(q)t(\000)t Fh(i)p FD(!)1972 3008 y FE(^)1962 3030 y FD(\036)p FB(p)p FD(!)s(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 3 w(;)g(v)s FB(q)p FE(.)34 b(W)-7 b(e)21 b(then)g(get)f(\()p 0 0.6 0 TeXcolorrgb 2913 3030 a SDict begin H.S end 2913 3030 a 0 0.6 0 TeXcolorrgb FE(4.3)p 0 0.6 0 TeXcolorrgb 3020 2977 a SDict begin H.R end 3020 2977 a 3020 3030 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.4.3) cvn H.B /ANN pdfmark end 3020 3030 a 0 TeXcolorgray FE(\).)0 3130 y FC(l)0 3221 y SDict begin H.S end 0 3221 a 0 3221 a SDict begin 12 H.A end 0 3221 a 0 3221 a SDict begin [/View [/XYZ H.V]/Dest (subsection.4.3) cvn /DEST pdfmark end 0 3221 a 150 3314 a FJ(4.3.)46 b(Probabilit)m(y)33 b(of)g(stic)m(king.)42 b FE(W)-7 b(e)29 b(are)e(in)n(terested)h(in)g(the)h(probabilit)n(y)24 b(of)29 b(stic)n(king,)0 3414 y(that)f(is)e(the)i(empirical)23 b(prop)r(ortion)j(of)h(time)f(sp)r(en)n(t)i(in)f(the)h(stic)n(king)d (phase:)954 3633 y SDict begin H.S end 954 3633 a 954 3633 a SDict begin 12 H.A end 954 3633 a 954 3633 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.5) cvn /DEST pdfmark end 954 3633 a 67 w FE(lim)968 3687 y Fy(T)9 b Fx(\321\0008)1222 3577 y FE(1)p 1213 3614 61 4 v 1213 3690 a FD(T)1297 3520 y Fr(\273)1359 3541 y Fy(T)1338 3709 y FG(0)1425 3633 y FJ(1)1473 3648 y Fy(D)1529 3632 y Fq(0)1566 3633 y FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1673 3599 a Fy(\016)1673 3654 y(t)1710 3633 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 1813 3599 a Fy(\016)1813 3654 y(t)1850 3633 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1953 3599 a Fy(\016)1953 3654 y(t)1990 3633 y FB(q)p FE(d)p FD(t;)783 b FE(\(4.5\))0 3848 y(where)24 b FD(D)308 3818 y FG(0)368 3848 y FB(\020)f(tp)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)613 3848 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)p FD(;)g(k)25 b FB(\020)e(\001)p FD(k)1104 3860 y Fy(\026)1144 3868 y Fq(s)1175 3848 y FD(;)14 b(:)g(:)g(:)g(;)g(k)1403 3860 y Fy(\026)1443 3868 y Fq(s)1474 3848 y FB(u)p FE(.)36 b(By)24 b(ergo)r(dicit)n(y)d (the)k(limit)c(\()p 0 0.6 0 TeXcolorrgb 2446 3848 a SDict begin H.S end 2446 3848 a 0 0.6 0 TeXcolorrgb FE(4.5)p 0 0.6 0 TeXcolorrgb 2553 3794 a SDict begin H.R end 2553 3794 a 2553 3848 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.4.5) cvn H.B /ANN pdfmark end 2553 3848 a 0 TeXcolorgray FE(\))j(exists)f(almost)0 3947 y(surely)-7 b(,)24 b(is)f(deterministic) e(and)j(its)g(v)-5 b(alue)24 b(is)f(indep)r(enden)n(t)i(of)f(the)h (starting)e(p)r(oin)n(t)h FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 2724 3917 a Fy(\016)2724 3968 y FG(0)2761 3947 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 2864 3917 a Fy(\016)2864 3968 y FG(0)2902 3947 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 3005 3917 a Fy(\016)3005 3968 y FG(0)3043 3947 y FB(q)0 4047 y FE(and)j(giv)n(en)f(b)n(y)862 4266 y SDict begin H.S end 862 4266 a 862 4266 a SDict begin 12 H.A end 862 4266 a 862 4266 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.6) cvn /DEST pdfmark end 862 4266 a FD(P)915 4278 y FG(stic)n(k)1076 4266 y FB(\020)1173 4205 y FA(E)1223 4217 y Fb(s)1254 4225 y Fd(\000)1311 4137 y Fr(\020)1345 4205 y FD(\034)1381 4217 y FG(1)1437 4205 y FB(\001)c FE(^)-46 b FD(\034)1556 4217 y FG(1)1593 4137 y Fr(\030)p 1173 4247 455 4 v 1261 4328 a FA(E)1310 4340 y Fb(s)1341 4348 y Fd(\000)1398 4260 y Fr(\020)1432 4328 y FD(\034)1468 4340 y FG(1)1506 4260 y Fr(\030)1661 4266 y FB(\020)22 b FE(1)c FB(\001)1901 4205 y FA(E)1950 4217 y Fb(s)1982 4225 y Fd(\000)2039 4137 y Fr(\020)2077 4205 y FE(^)-46 b FD(\034)2109 4217 y FG(1)2146 4137 y Fr(\030)p 1901 4247 280 4 v 1901 4328 a FA(E)1950 4340 y Fb(s)1982 4348 y Fd(\000)2039 4260 y Fr(\020)2073 4328 y FD(\034)2109 4340 y FG(1)2146 4260 y Fr(\030)2190 4266 y FD(:)691 b FE(\(4.6\))0 4485 y(This)27 b(n)n(um)n(b)r(er)f(can)h(b)r (e)h(ev)-5 b(aluated)26 b(as)h(follo)n(ws.)1501 4485 y SDict begin H.S end 1501 4485 a 1501 4485 a SDict begin 12 H.A end 1501 4485 a 1501 4485 a SDict begin [/View [/XYZ H.V]/Dest (thm.4.1) cvn /DEST pdfmark end 1501 4485 a 150 4585 a Fg(Pr)n(oposition)21 b(4.1.)37 b 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FB(u)p Fz(,)0 4685 y(b)l(e)30 b(the)g(solutions)g(of) 571 4847 y Fe(L)639 4826 y FE(^)p 0 TeXcolorgray 628 4847 a FD(R)p 0 TeXcolorgray 24 w FB(\020)22 b(\001)p FE(1)48 b Fz(in)g FD(E)5 b FB(z)p FD(D)1250 4813 y FG(0)1287 4847 y FD(;)1505 4826 y FE(^)p 0 TeXcolorgray 1493 4847 a FD(R)p 0 TeXcolorgray 24 w FB(\020)23 b FE(0)47 b Fz(in)i FD(D)1949 4813 y FG(0)1986 4847 y FD(;)2904 4847 y SDict begin H.S end 2904 4847 a 2904 4847 a SDict begin 15 H.A end 2904 4847 a 2904 4847 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.7) cvn /DEST pdfmark end 2904 4847 a FE(\(4.7\))571 4983 y Fe(L)639 4962 y FE(\024)p 0 TeXcolorgray 628 4983 a FD(R)p 0 TeXcolorgray 24 w FB(\020)22 b(\001)p FE(1)48 b Fz(in)g FD(E)5 b FB(ztp)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\010)p Fy(k)1381 5003 y Fp(\026)1416 5011 y Fq(s)1452 4983 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(qu)p FD(;)1896 4962 y FE(\024)p 0 TeXcolorgray 1884 4983 a FD(R)p 0 TeXcolorgray 1 w FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2028 4995 a Fx(\010)p Fy(k)2114 5003 y Fp(\026)2149 5011 y Fq(s)2185 4983 y FD(;)g FE(0)p FD(;)g FE(0)p FB(q)22 b(\020)g FE(0)p FD(;)2904 4983 y SDict begin H.S end 2904 4983 a 2904 4983 a SDict begin 15 H.A end 2904 4983 a 2904 4983 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.8) cvn /DEST pdfmark end 2904 4983 a FE(\(4.8\))526 5121 y FD(Q)592 5087 y Fy(\016)p 0 TeXcolorgray 628 5121 a FD(R)p 0 TeXcolorgray 24 w FB(\020)g(\001)p FE(1)48 b Fz(in)g FB(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)1247 5141 y Fp(\026)1282 5149 y Fq(s)1318 5121 y FD(;)14 b(:)g(:)g(:)g(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 12 x Fy(k)1585 5141 y Fp(\026)1620 5149 y Fq(s)1656 5121 y FB(u)p FD(;)p 0 TeXcolorgray 183 w(R)p 0 TeXcolorgray 1 w FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 2043 5137 a Fx(\010p)p Fy(k)2155 5145 y Fp(\026)2194 5137 y Fx(\000)p FG(1)p Fx(q)2308 5121 y FB(q)24 b(\020)e FE(0)p FD(:)2904 5121 y SDict begin H.S end 2904 5121 a 2904 5121 a SDict begin 15 H.A end 2904 5121 a 2904 5121 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.9) cvn /DEST pdfmark end 2904 5121 a FE(\(4.9\))p 0 TeXcolorgray 0 TeXcolorgray eop end end %%Page: 13 13 TeXDict begin HPSdict begin 13 12 bop 0 TeXcolorgray 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a 0 TeXcolorgray -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.13) cvn /DEST pdfmark end -8 -8 a 0 TeXcolorgray 0 TeXcolorgray 1050 83 a FI(Dry)23 b(friction)i(problem)f(with)h(noise)968 b FE(13)p 0 TeXcolorgray 0 286 a Fz(Then)30 b(we)g(have)h FA(E)580 298 y Fb(s)611 306 y Fd(\000)668 218 y Fr(\020)706 286 y FE(^)-46 b FD(\034)738 298 y FG(1)776 218 y Fr(\030)833 286 y FB(\020)931 265 y FE(^)p 0 TeXcolorgray 920 286 a FD(R)p 0 TeXcolorgray 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918 y FB(p)p Fs(s)777 930 y Fx(\000)832 918 y FD(;)c FJ(1)917 933 y Fy(D)973 916 y Fq(0)1009 918 y FB(q)p FE(,)30 b(where)e FD(w)1394 930 y FG(0)1460 918 y FE(has)g(b)r(een)h(in)n(tro)r(duced)f(in)g(\()p 0 0.6 0 TeXcolorrgb 2353 918 a SDict begin H.S end 2353 918 a 0 0.6 0 TeXcolorrgb FE(3.6)p 0 0.6 0 TeXcolorrgb 2460 865 a SDict begin H.R end 2460 865 a 2460 918 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.6) cvn H.B /ANN pdfmark end 2460 918 a 0 TeXcolorgray FE(\),)g(so)g(that)h(w)n(e)f(can)0 1018 y(also)e(write)82 1231 y SDict begin H.S end 82 1231 a 82 1231 a SDict begin 12 H.A end 82 1231 a 82 1231 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.11) cvn /DEST pdfmark end 82 1231 a FD(P)135 1243 y FG(stic)n(k)296 1231 y FB(\020)d FE(1)18 b FB(\001)802 1169 y FD(w)861 1181 y FG(0)899 1169 y FB(p)p Fs(s)968 1181 y Fx(\000)1023 1169 y FD(;)c FJ(1)1108 1184 y Fy(E)s Fx(z)p Fy(D)1242 1168 y Fq(0)1279 1169 y FB(q)p 537 1212 1041 4 v 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FB(q)28 b FE(for)f(an)n(y)p 0 TeXcolorgray 27 w FD(x)p 0 TeXcolorgray 24 w FB(P)d(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)2093 1961 y Fp(\026)2128 1969 y Fq(s)2164 1941 y FD(;)14 b(:)g(:)g(:)f(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 2396 1953 a Fy(k)2431 1961 y Fp(\026)2466 1969 y Fq(s)2501 1941 y FB(u)p FE(.)38 b(Moreo)n(v)n(er,)25 b(b)n(y)0 2041 y(the)j(strong)e(Mark)n(o)n(v)g (prop)r(ert)n(y)-7 b(,)0 2221 y FA(E)49 2233 y Fb(s)81 2241 y Fd(\000)138 2153 y Fr(\020)172 2221 y FD(\034)208 2233 y FG(1)245 2153 y Fr(\030)302 2221 y FB(\020)23 b FA(E)439 2233 y Fb(s)471 2241 y Fd(\000)528 2153 y Fr(\020)566 2221 y FE(\024)-46 b FD(\034)598 2233 y FG(1)635 2153 y Fr(\030)688 2221 y FB(\000)18 b FA(E)820 2233 y Fb(s)851 2241 y Fd(\000)908 2153 y Fr(\020)942 2221 y FA(E)9 b FB(r)p FD(\034)1057 2233 y FG(1)1118 2221 y FB(\001)23 b FE(\024)-47 b FD(\034)1237 2233 y FG(1)1275 2221 y FB(|)t FE(\024)h FD(\034)1334 2233 y FG(1)1371 2221 y FB(s)1400 2153 y Fr(\030)302 2358 y 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y Fr(\000)p 0 TeXcolorgray 68 x FD(X)p 0 TeXcolorgray 2751 2324 a Fy(\016)2755 2379 y FG(\024)-37 b Fy(\034)2782 2387 y Fq(1)2841 2358 y FB(\020)p 0 TeXcolorgray 23 w FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)3062 2378 y Fp(\026)3097 2386 y Fq(s)3133 2290 y Fr(\010)3171 2358 y FD(:)0 2559 y FE(By)18 b(symmetry)e(of)i(the)h(system)e(w)n(e)h(ha)n(v)n(e)f FA(E)1330 2574 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 1399 2583 a Fd(\001)p Fp(k)1473 2591 y(\026)1508 2599 y Fq(s)1544 2574 y Fy(;)p FG(0)p Fy(;)p FG(0)p Fx(q)1680 2559 y FB(r)p FD(\034)1745 2571 y FG(1)1782 2559 y FB(s)22 b(\020)h FA(E)1970 2574 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 2040 2583 a Fp(k)2071 2591 y(\026)2106 2599 y Fq(s)2142 2574 y Fy(;)p FG(0)p Fy(;)p FG(0)p Fx(q)2278 2559 y FB(r)p FD(\034)2343 2571 y FG(1)2380 2559 y FB(s)p FE(,)d(so)d(that)i FA(E)2764 2571 y Fb(s)2796 2579 y Fd(\000)2853 2491 y Fr(\020)2887 2559 y FD(\034)2923 2571 y FG(1)2960 2491 y Fr(\030)3017 2559 y FB(\020)0 2678 y FA(E)49 2690 y Fb(s)81 2698 y Fd(\000)138 2610 y Fr(\020)176 2678 y FE(\024)-46 b FD(\034)208 2690 y FG(1)245 2610 y Fr(\030)298 2678 y FB(\000)18 b FA(E)430 2694 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 500 2703 a Fp(k)531 2711 y(\026)566 2719 y Fq(s)602 2694 y Fy(;)p FG(0)p Fy(;)p FG(0)p Fx(q)737 2610 y Fr(\020)772 2678 y FD(\034)808 2690 y FG(1)845 2610 y Fr(\030)907 2678 y FE(and)27 b(w)n(e)g(get)1029 2881 y FA(E)1079 2893 y Fb(s)1110 2901 y Fd(\000)1167 2813 y Fr(\020)1201 2881 y FD(\034)1237 2893 y FG(1)1275 2813 y Fr(\030)1332 2881 y FB(\020)1431 2860 y FE(\024)p 0 TeXcolorgray 1419 2881 a FD(R)p 0 TeXcolorgray 1 w FB(p)p Fs(s)1552 2893 y Fx(\000)1607 2881 y FB(q)19 b(\000)p 0 TeXcolorgray 18 w FD(R)p 0 TeXcolorgray 1 w FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)1919 2901 y Fp(\026)1954 2909 y Fq(s)1990 2881 y FB(q)p FD(;)0 3061 y FE(whic)n(h)27 b(completes)e(the)j(pro)r(of)f(of)g(the)h(prop)r(osition.)p 1687 3010 39 5 v 1687 3056 5 47 v 1721 3056 V 1687 3061 39 5 v 0 3124 a SDict begin H.S end 0 3124 a 0 3124 a SDict begin 12 H.A end 0 3124 a 0 3124 a SDict begin [/View [/XYZ H.V]/Dest (subsection.4.4) cvn /DEST pdfmark end 0 3124 a 150 3207 a FJ(4.4.)46 b(Distributions)40 b(of)i(stic)m(king)f (and)i(sliding)c(p)s(erio)s(ds.)45 b FE(The)36 b(dynamics)e(of)i(the)0 3307 y(system)g(consists)f(of)i(an)f(alternate)f(sequence)i(of)g(stic)n (king)d(p)r(erio)r(ds)h(and)i(sliding)d(\(dynamic\))0 3406 y(p)r(erio)r(ds.)69 b(Eac)n(h)37 b(sliding)f(p)r(erio)r(d)h (starts)h(from)f Fs(s)1605 3418 y Fx(\010)1699 3406 y FE(and)h(the)h(system)f(is)f(symmetric)f(for)i(the)0 3506 y(transform)29 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)30 b(\321)f(p\001)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)14 b FB(\001)p 0 TeXcolorgray FD(y)p 0 TeXcolorgray 2 w(;)g FB(\001)p FD(v)s FB(q)p FE(.)48 b(As)31 b(a)g(result)f(the)i(Laplace)d(transform)h(of)h(the)h (distri-)0 3606 y(bution)27 b(of)g(the)h(duration)e(of)i(a)f(stic)n (king)e(p)r(erio)r(d)i(is)1035 3786 y SDict begin H.S end 1035 3786 a 1035 3786 a SDict begin 12 H.A end 1035 3786 a 1035 3786 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.12) cvn /DEST pdfmark end 1035 3786 a FD(F)1088 3798 y FG(stic)n(k)1226 3786 y FB(p)p FD(\025)p FB(q)d(\020)f FA(E)1499 3798 y Fb(s)1530 3806 y Fd(\000)1587 3718 y Fr(\020)1621 3786 y FD(e)1660 3751 y Fx(\001)p Fy(\025)p Fx(p)p Fy(\034)1807 3759 y Fq(1)1839 3751 y Fx(\001)t FG(^)-37 b Fy(\034)1921 3759 y Fq(1)1953 3751 y Fx(q)1983 3718 y Fr(\030)2017 3786 y FD(:)823 b FE(\(4.12\))0 3966 y(This)27 b(Laplace)e(transform)h(can)h(b)r(e)h(ev)-5 b(aluated)26 b(as)h(follo)n(ws.)1886 3966 y SDict begin H.S end 1886 3966 a 1886 3966 a SDict begin 12 H.A end 1886 3966 a 1886 3966 a SDict begin [/View [/XYZ H.V]/Dest (thm.4.2) cvn /DEST pdfmark end 1886 3966 a 150 4066 a Fg(Pr)n(oposition)37 b(4.2.)60 b Fz(F)-6 b(or)35 b FB(|)p FD(k)s FB(|)f(\244)f FD(k)1323 4078 y Fy(\026)1363 4086 y Fq(s)1430 4066 y Fz(and)j FD(\025)e FB(\241)e FE(0)p Fz(,)37 b(let)2021 4045 y FE(^)2003 4066 y FD(P)2056 4078 y Fy(k)2097 4066 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)p Fz(,)38 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)34 b(P)f FD(E)5 b Fz(,)37 b(and)0 4165 y FD(F)53 4177 y Fy(\025)97 4165 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)p Fz(,)p 0 TeXcolorgray 30 w FD(x)p 0 TeXcolorgray 24 w FB(P)22 b(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 486 4177 a Fx(\001)p Fy(k)572 4185 y Fp(\026)607 4193 y Fq(s)638 4177 y Fx(\001)p FG(1)727 4165 y FD(;)14 b(:)g(:)g(:)f(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 959 4177 a Fy(k)994 4185 y Fp(\026)1029 4193 y Fq(s)1060 4177 y Fx(\000)p FG(1)1148 4165 y FB(u)30 b Fz(b)l(e)g(the)g(solutions)g(of)123 4362 y Fe(L)199 4341 y FE(^)180 4362 y FD(P)233 4374 y Fy(k)298 4362 y FB(\020)22 b FE(0)48 b Fz(in)g FD(E)5 b FB(z)p FD(D)768 4327 y FG(0)805 4362 y FD(;)1030 4341 y FE(^)1012 4362 y FD(P)1065 4374 y Fy(k)1106 4362 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1186 4374 a Fy(k)1227 4362 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(q)22 b(\020)g FE(1)p FD(;)1793 4341 y FE(^)1774 4362 y FD(P)1827 4374 y Fy(k)1892 4362 y FB(\020)g FE(0)48 b Fz(in)g FD(D)2260 4327 y FG(0)2298 4362 y FB(ztp)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fy(k)2491 4362 y FD(;)14 b FE(0)p FD(;)g FE(0)p FB(qu)p FD(;)2863 4362 y SDict begin H.S end 2863 4362 a 2863 4362 a SDict begin 15 H.A end 2863 4362 a 2863 4362 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.13) cvn /DEST pdfmark end 2863 4362 a FE(\(4.13\))123 4499 y FD(\025F)224 4511 y Fy(\025)287 4499 y FB(\001)k FD(Q)436 4465 y Fy(\016)472 4499 y FD(F)525 4511 y Fy(\025)592 4499 y FB(\020)23 b FE(0)47 b Fz(in)i FB(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)1060 4519 y Fp(\026)1095 4527 y Fq(s)1131 4499 y FD(;)14 b(:)g(:)g(:)f(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 1363 4511 a Fy(k)1398 4519 y Fp(\026)1433 4527 y Fq(s)1469 4499 y FB(u)18 b FD(;)183 b(F)1783 4511 y Fy(\025)1827 4499 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1907 4515 a Fx(\010p)p Fy(k)2019 4523 y Fp(\026)2054 4531 y Fq(s)2086 4515 y Fx(\000)p FG(1)p Fx(q)2200 4499 y FB(q)23 b(\020)g FE(1)p FD(:)2863 4499 y SDict begin H.S end 2863 4499 a 2863 4499 a SDict begin 15 H.A end 2863 4499 a 2863 4499 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.14) cvn /DEST pdfmark end 2863 4499 a FE(\(4.14\))0 4699 y Fz(Then)i(we)f(have)i FA(P)566 4711 y Fb(s)597 4719 y Fd(\000)646 4631 y Fr(\000)p 0 TeXcolorgray 68 x FD(X)p 0 TeXcolorgray 760 4669 a Fy(\016)764 4722 y FG(^)-37 b Fy(\034)791 4730 y Fq(1)850 4699 y FB(\020)p 0 TeXcolorgray 23 w FD(x)p 0 TeXcolorgray 12 x Fy(k)1026 4631 y Fr(\010)1087 4699 y FB(\020)1193 4678 y FE(^)1175 4699 y FD(P)1228 4711 y Fy(k)1269 4699 y FB(p)p Fs(s)1338 4711 y Fx(\000)1393 4699 y FB(q)24 b Fz(for)h(any)g FD(k)h FB(P)d(t\001)p FD(k)2011 4711 y Fy(\026)2051 4719 y Fq(s)2082 4699 y FD(;)14 b(:)g(:)g(:)f(;)h(k)2309 4711 y Fy(\026)2349 4719 y Fq(s)2381 4699 y FB(u)p Fz(,)25 b FA(E)2518 4714 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 5 w(;)p FG(0)p Fy(;)p FG(0)p Fx(q)2723 4631 y Fr(\020)2757 4699 y FD(e)2796 4669 y Fx(\001)p Fy(\025\034)2917 4677 y Fq(1)2953 4631 y Fr(\030)3010 4699 y FB(\020)0 4799 y FD(F)53 4811 y Fy(\025)97 4799 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w FB(q)30 b Fz(for)g(any)p 0 TeXcolorgray 30 w FD(x)p 0 TeXcolorgray 24 w FB(P)23 b(t)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 12 x Fx(\001)p Fy(k)838 4819 y Fp(\026)873 4827 y Fq(s)909 4799 y FD(;)14 b(:)g(:)g(:)f(;)p 0 TeXcolorgray 14 w(x)p 0 TeXcolorgray 1141 4811 a Fy(k)1176 4819 y Fp(\026)1211 4827 y Fq(s)1247 4799 y FB(u)29 b Fz(and)h FD(\025)24 b FB(\241)f FE(0)p Fz(,)29 b(and)941 5074 y SDict begin H.S end 941 5074 a 941 5074 a SDict begin 12 H.A end 941 5074 a 941 5074 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.15) cvn /DEST pdfmark end 941 5074 a FD(F)994 5086 y FG(stic)n(k)1133 5074 y FB(p)p FD(\025)p FB(q)24 b(\020)1425 4965 y Fy(k)1460 4973 y Fp(\026)1495 4981 y Fq(s)1430 4995 y Fr(\270)1356 5170 y Fy(k)q Fx(\020\001)p Fy(k)1529 5178 y Fp(\026)1564 5186 y Fq(s)1610 5074 y FD(F)1663 5086 y Fy(\025)1707 5074 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1787 5086 a Fy(k)1828 5074 y FB(q)1879 5053 y FE(^)1860 5074 y FD(P)1913 5086 y Fy(k)1954 5074 y FB(p)p Fs(s)2023 5086 y Fx(\000)2078 5074 y FB(q)p FD(:)730 b FE(\(4.15\))p 0 TeXcolorgray 0 TeXcolorgray eop end end %%Page: 14 14 TeXDict begin HPSdict begin 14 13 bop 0 TeXcolorgray 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a 0 TeXcolorgray -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.14) cvn /DEST pdfmark end -8 -8 a 0 TeXcolorgray 0 TeXcolorgray 0 83 a FE(14)965 b FI(J.)23 b(Garnier,)h(Z.)f(Lu,)h(and)g(L.)f(Mertz)p 0 TeXcolorgray 150 386 a Fz(Pr)l(o)l(of)p FE(.)38 b(This)27 b(is)f(a)h(consequence)g(of)h(the)g(strong)e(Mark)n(o)n(v)f(prop)r(ert) n(y:)105 631 y FD(F)158 643 y FG(stic)n(k)296 631 y FB(p)p FD(\025)p FB(q)f(\020)f FA(E)569 643 y Fb(s)601 651 y Fd(\000)658 563 y Fr(\020)692 631 y FA(E)8 b FB(r)p FD(e)809 597 y Fx(\001)p Fy(\025)p Fx(p)p Fy(\034)956 605 y Fq(1)994 597 y Fx(\001)t FG(^)-37 b Fy(\034)1076 605 y Fq(1)1107 597 y Fx(q)1138 631 y FB(|)t FE(^)-46 b FD(\034)1197 643 y FG(1)1234 631 y FD(;)p 0 TeXcolorgray 14 w(X)p 0 TeXcolorgray 1346 597 a Fy(\016)1350 651 y FG(^)-37 b Fy(\034)1377 659 y Fq(1)1414 631 y FB(s)1443 563 y Fr(\030)1499 631 y FB(\020)1656 522 y Fy(k)1691 530 y Fp(\026)1726 538 y Fq(s)1661 552 y Fr(\270)1587 726 y Fy(k)q Fx(\020\001)p Fy(k)1760 734 y Fp(\026)1795 742 y Fq(s)1841 631 y FA(P)1893 643 y Fb(s)1924 651 y Fd(\000)1974 563 y Fr(\000)p 0 TeXcolorgray 68 x FD(X)p 0 TeXcolorgray 2087 597 a Fy(\016)2091 651 y FG(^)g Fy(\034)2118 659 y Fq(1)2178 631 y FB(\020)p 0 TeXcolorgray 22 w FD(x)p 0 TeXcolorgray 2313 643 a Fy(k)2353 563 y Fr(\010)2391 631 y FA(E)2441 646 y Fx(p)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray 2510 655 a Fp(k)2547 646 y Fy(;)p FG(0)p Fy(;)p FG(0)p Fx(q)2682 563 y Fr(\020)2717 631 y FD(e)2756 597 y Fx(\001)p Fy(\025\034)2877 605 y Fq(1)2913 563 y Fr(\030)2947 631 y FD(:)p 0 828 39 5 v 0 874 5 47 v 34 874 V 0 879 39 5 v 150 979 a FE(Similarly)29 b(the)34 b(Laplace)e(transform)g(of)i(the)h(distribution)c(of)j(the)g(duration)f (of)h(a)f(sliding)0 1079 y(p)r(erio)r(d)27 b(is)1119 1241 y SDict begin H.S end 1119 1241 a 1119 1241 a SDict begin 12 H.A end 1119 1241 a 1119 1241 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.16) cvn /DEST pdfmark end 1119 1241 a FD(F)1172 1253 y FG(slide)1307 1241 y FB(p)p FD(\025)p FB(q)d(\020)f FA(E)1580 1253 y Fb(s)1611 1261 y Fd(\000)1668 1173 y Fr(\020)1702 1241 y FD(e)1741 1207 y Fx(\001)p Fy(\025)t FG(^)-37 b Fy(\034)1862 1215 y Fq(1)1898 1173 y Fr(\030)1933 1241 y FD(;)907 b FE(\(4.16\))0 1404 y(and)27 b(it)g(can)h(b)r(e)g(expressed)e(as)h(follo)n(ws.)1255 1404 y SDict begin H.S end 1255 1404 a 1255 1404 a SDict begin 12 H.A end 1255 1404 a 1255 1404 a SDict begin [/View [/XYZ H.V]/Dest (thm.4.3) cvn /DEST pdfmark end 1255 1404 a 150 1504 a Fg(Pr)n(oposition)k(4.3.)40 b Fz(F)-6 b(or)30 b FD(\025)23 b FB(\241)g FE(0)p Fz(,)30 b(let)f FD(G)1462 1516 y Fy(\025)1506 1504 y FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)p Fz(,)31 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)p 0 TeXcolorgray 14 w(y)p 0 TeXcolorgray 2 w(;)14 b(v)s FB(q)24 b(P)f FD(E)34 b Fz(b)l(e)c(the)g(solution)g(of)658 1667 y SDict begin H.S end 658 1667 a 658 1667 a SDict begin 12 H.A end 658 1667 a 658 1667 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.17) cvn /DEST pdfmark end 658 1667 a FD(\025G)771 1679 y Fy(\025)833 1667 y FB(\001)18 b Fe(L)p FD(G)1038 1679 y Fy(\025)1106 1667 y FB(\020)k FE(0)48 b Fz(in)g FD(E)5 b FB(z)p FD(D)1576 1632 y FG(0)1631 1667 y FD(;)184 b(G)1903 1679 y Fy(\025)1970 1667 y FB(\020)23 b FE(1)47 b Fz(in)h FD(D)2338 1632 y FG(0)2394 1667 y FD(:)446 b FE(\(4.17\))0 1829 y Fz(Then)30 b(we)g(have)1188 1992 y SDict begin H.S end 1188 1992 a 1188 1992 a SDict begin 12 H.A end 1188 1992 a 1188 1992 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.18) cvn /DEST pdfmark end 1188 1992 a FD(F)1241 2004 y FG(slide)1375 1992 y FB(p)p FD(\025)p FB(q)24 b(\020)f FD(G)1664 2004 y Fy(\025)1708 1992 y FB(p)p Fs(s)1777 2004 y Fx(\000)1832 1992 y FB(q)p FD(:)976 b FE(\(4.18\))150 2255 y(F)-7 b(rom)26 b(\()p 0 0.6 0 TeXcolorrgb 400 2255 a SDict begin H.S end 400 2255 a 0 0.6 0 TeXcolorrgb FE(3.6)p 0 0.6 0 TeXcolorrgb 507 2201 a SDict begin H.R end 507 2201 a 507 2255 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.6) cvn H.B /ANN pdfmark end 507 2255 a 0 TeXcolorgray FE(\))h(w)n(e)h(also)d(ha)n(v)n(e)208 2480 y FD(w)267 2492 y Fy(\025)311 2480 y FB(p)p Fs(s)380 2492 y Fx(\000)436 2480 y FD(;)14 b FJ(1)521 2495 y Fy(E)s Fx(z)p Fy(D)655 2478 y Fq(0)691 2480 y FB(q)23 b(\020)g FA(E)883 2492 y Fb(s)915 2500 y Fd(\000)971 2387 y Fr(\021)1025 2367 y(\273)1087 2387 y Fy(\034)1118 2395 y Fq(1)1066 2555 y FG(0)1168 2480 y FD(e)1207 2445 y Fx(\001)p Fy(\025s)1333 2480 y FJ(1)1381 2495 y Fy(E)s Fx(z)p Fy(D)1515 2478 y Fq(0)1551 2480 y FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1659 2445 a Fy(\016)1659 2500 y(s)1695 2480 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 1799 2445 a Fy(\016)1799 2500 y(s)1835 2480 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1939 2445 a Fy(\016)1939 2500 y(s)1975 2480 y FB(q)p FE(d)q FD(s)2093 2387 y Fr(\031)2156 2480 y FB(\020)f FA(E)2292 2492 y Fb(s)2324 2500 y Fd(\000)2381 2387 y Fr(\021)2434 2367 y(\273)2500 2387 y FG(^)-37 b Fy(\034)2527 2395 y Fq(1)2476 2555 y FG(0)2577 2480 y FD(e)2616 2445 y Fx(\001)p Fy(\025s)2742 2480 y FE(d)p FD(s)2827 2387 y Fr(\031)746 2698 y FB(\020)847 2642 y FE(1)p 844 2679 49 4 v 844 2755 a FD(\025)902 2630 y Fr(\000)940 2698 y FE(1)18 b FB(\001)g FA(E)1133 2710 y Fb(s)1164 2718 y Fd(\000)1221 2630 y Fr(\020)1255 2698 y FD(e)1294 2664 y Fx(\001)p Fy(\025)t FG(^)-37 b Fy(\034)1415 2672 y Fq(1)1451 2630 y Fr(\030\010)1523 2698 y FD(;)2863 2698 y SDict begin H.S end 2863 2698 a 2863 2698 a SDict begin 15 H.A end 2863 2698 a 2863 2698 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.19) cvn /DEST pdfmark end 2863 2698 a FE(\(4.19\))0 2889 y(so)27 b(that)h(w)n(e)f(get)g FD(F)595 2901 y FG(slide)730 2889 y FB(p)p FD(\025)p FB(q)d(\020)f FE(1)18 b FB(\001)g FD(\025w)1204 2901 y Fy(\025)1248 2889 y FB(p)p Fs(s)1317 2901 y Fx(\000)1372 2889 y FD(;)c FJ(1)1457 2904 y Fy(E)s Fx(z)p Fy(D)1591 2888 y Fq(0)1628 2889 y FB(q)p FE(.)0 2962 y SDict begin H.S end 0 2962 a 0 2962 a SDict begin 12 H.A end 0 2962 a 0 2962 a SDict begin [/View [/XYZ H.V]/Dest (section.5) cvn /DEST pdfmark end 0 2962 a 150 3031 a FJ(5.)47 b(Numerics.)42 b FE(In)33 b(this)g(section,)g(w)n(e)f(are)g(in)n (terested)g(in)g(the)h(n)n(umerical)c(computation)0 3131 y(of)f(the)g(follo)n(wing)23 b(statistics)i(under)j(the)g(stationary)d (measure:)511 3294 y SDict begin H.S end 511 3294 a 511 3294 a SDict begin 12 H.A end 511 3294 a 511 3294 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.1) cvn /DEST pdfmark end 511 3294 a -90 w FD(S)477 3260 y FG(1)537 3294 y FB(\020)e FD(P)678 3306 y FG(stic)n(k)816 3294 y FD(;)180 b(S)1075 3260 y FG(2)1135 3294 y FB(\020)23 b FA(E)1272 3306 y Fy(\031)1323 3294 y FB(rp)p 0 TeXcolorgray FD(V)p 0 TeXcolorgray 1451 3260 a Fy(\016)1451 3314 y(t)1487 3294 y FB(q)1519 3260 y FG(2)1557 3294 y FB(s)p FD(;)179 b(S)1844 3260 y FG(3)1904 3294 y FB(\020)23 b FA(P)2044 3306 y Fy(\031)2102 3226 y Fr(\000)2140 3294 y FB(|)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 2238 3260 a Fy(\016)2238 3314 y(t)2274 3294 y FB(|)h(\244)e FD(\026)2458 3306 y FG(s)2489 3226 y Fr(\010)2541 3294 y FD(:)340 b FE(\(5.1\))0 3457 y(W)-7 b(e)37 b(use)f(t)n(w)n(o)f(di\013eren)n(t)g(metho)r(ds.)62 b(The)36 b(\014rst)g(metho)r(d)g(is)f(probabilistic)c(and)36 b(relies)e(on)i(the)0 3556 y(represen)n(tation)19 b(form)n(ula)h(\()p 0 0.6 0 TeXcolorrgb 869 3556 a SDict begin H.S end 869 3556 a 0 0.6 0 TeXcolorrgb FE(4.1)p 0 0.6 0 TeXcolorrgb 976 3503 a SDict begin H.R end 976 3503 a 976 3556 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.4.1) cvn H.B /ANN pdfmark end 976 3556 a 0 TeXcolorgray FE(\))h(of)h FD(S)1174 3526 y Fy(i)1224 3556 y FE(in)f(terms)g(of)h(the)h(excursions)c FB(tp)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 2307 3526 a Fy(\016)2307 3577 y(s)2343 3556 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 2447 3526 a Fy(\016)2447 3577 y(s)2483 3556 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 2587 3526 a Fy(\016)2587 3577 y(s)2623 3556 y FB(q)p FD(;)j(s)h FB(P)g(r)p FE(0)p FD(;)14 b(\034)2973 3568 y FG(1)3010 3556 y FB(su)0 3656 y FE(starting)21 b(from)g Fs(s)533 3668 y Fx(\000)588 3656 y FE(.)36 b FD(S)703 3626 y FG(1)740 3656 y FE(,)23 b(resp.)35 b FD(S)1049 3626 y FG(2)1109 3656 y FE(and)23 b FD(S)1322 3626 y FG(3)1358 3656 y FE(,)h(has)f(the)g(form)e(\()p 0 0.6 0 TeXcolorrgb 1910 3656 a SDict begin H.S end 1910 3656 a 0 0.6 0 TeXcolorrgb FE(4.1)p 0 0.6 0 TeXcolorrgb 2017 3602 a SDict begin H.R end 2017 3602 a 2017 3656 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.4.1) cvn H.B /ANN pdfmark end 2017 3656 a 0 TeXcolorgray FE(\))i(with)f FD(f)9 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)14 b(v)s FB(q)24 b(\020)e FJ(1)2656 3671 y Fx(t)p Fy(v)r Fx(\020)p FG(0)p Fy(;)p Fx(|)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray -1 w Fx(|\244)p Fy(\026)2991 3679 y Fq(s)3018 3671 y Fx(u)3052 3656 y FE(,)0 3756 y(resp.)47 b FD(f)9 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)14 b(v)s FB(q)30 b(\020)f FD(v)627 3725 y FG(2)695 3756 y FE(and)i FD(f)9 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray 1 w(;)14 b(v)s FB(q)29 b(\020)g FJ(1)1273 3771 y Fx(t|)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray -1 w Fx(|\244)p Fy(\026)1469 3779 y Fq(s)1496 3771 y Fx(u)1529 3756 y FE(.)48 b(The)31 b(second)g(metho)r(d)g(is)f(deterministic)d(and)0 3855 y(consists)j(in)i(solving)d(the)j(equation)f(\()p 0 0.6 0 TeXcolorrgb 1219 3855 a SDict begin H.S end 1219 3855 a 0 0.6 0 TeXcolorrgb FE(3.2)p 0 0.6 0 TeXcolorrgb 1326 3802 a SDict begin H.R end 1326 3802 a 1326 3855 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.3.2) cvn H.B /ANN pdfmark end 1326 3855 a 0 TeXcolorgray FE(\))h(with)g FD(f)40 b FE(in)32 b(the)g(righ)n(t-hand)e(side)h(and)h(w)n(e)g(lo)r (ok)f(for)0 3955 y FD(\025u)96 3967 y Fy(\025)139 3955 y FB(p)p FD(f)9 b FB(q)28 b FE(for)f(small)e FD(\025)p FE(.)0 4019 y SDict begin H.S end 0 4019 a 0 4019 a SDict begin 12 H.A end 0 4019 a 0 4019 a SDict begin [/View [/XYZ H.V]/Dest (subsection.5.1) cvn /DEST pdfmark end 0 4019 a 150 4097 a FJ(5.1.)46 b(The)22 b(probabilistic)e(metho)s(d:)34 b(sim)m(ulation)19 b(of)i(the)g(excursions)g(of)g FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 2813 4067 a Fy(\016)2813 4118 y(s)2849 4097 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 2953 4067 a Fy(\016)2953 4118 y(s)2989 4097 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 3093 4067 a Fy(\016)3093 4118 y(s)3129 4097 y FB(q)0 4197 y FJ(on)36 b FB(r)p FE(0)p FD(;)14 b(\034)281 4209 y FG(1)318 4197 y FB(s)p FJ(.)43 b FE(W)-7 b(e)31 b(generate)g(a)g(large) e(n)n(um)n(b)r(er,)i(sa)n(y)p 0 TeXcolorgray 30 w FD(M)p 0 TeXcolorgray 9 w FE(,)h(of)g(indep)r(enden)n(t)f(and)g(iden)n (tically)c(dis-)0 4297 y(tributed)18 b(\(i.i.d.\))33 b(v)n(ersions)15 b(of)k(the)f(excursions)e FB(tp)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1634 4267 a Fy(\016)1634 4317 y(s)1670 4297 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 1774 4267 a Fy(\016)1774 4317 y(s)1810 4297 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1914 4267 a Fy(\016)1914 4317 y(s)1950 4297 y FB(q)p FD(;)e(s)23 b FB(P)g(r)p FE(0)p FD(;)14 b(\034)2292 4309 y FG(1)2329 4297 y FB(su)k FE(where)g FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 2751 4267 a Fy(\016)2751 4317 y FG(0)2788 4297 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 2892 4267 a Fy(\016)2892 4317 y FG(0)2929 4297 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 3033 4267 a Fy(\016)3033 4317 y FG(0)3070 4297 y FB(q)24 b(\020)0 4396 y Fs(s)37 4408 y Fx(\000)92 4396 y FE(.)37 b(F)-7 b(rom)26 b(this)h(family)e(of)i (excursions,)e(w)n(e)j(construct)p 0 TeXcolorgray 27 w FD(M)p 0 TeXcolorgray 36 w FE(i.i.d.)35 b(v)n(ersions)25 b FB(t)p 0 TeXcolorgray Fh(\030)p 0 TeXcolorgray 2503 4366 a Fx(p)p Fy(i)p Fx(q)2582 4396 y FB(u)2619 4366 y Fy(M)2619 4418 y(i)p Fx(\020)p FG(1)2758 4396 y FE(of)807 4607 y SDict begin H.S end 807 4607 a 807 4607 a SDict begin 12 H.A end 807 4607 a 807 4607 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.2) cvn /DEST pdfmark end 807 4607 a 0 TeXcolorgray Fh(\030)h FB(\020)d(p)p FD(\030)1031 4619 y FG(1)1069 4607 y FD(;)14 b(\030)1142 4619 y FG(2)1179 4607 y FB(q)1211 4573 y Fy(T)p 0 TeXcolorgray 1287 4607 a FB(\020)1374 4514 y Fr(\001)1438 4494 y(\273)1500 4514 y Fy(\034)1531 4522 y Fq(1)1479 4683 y FG(0)1581 4607 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1738 4573 a Fy(\016)1738 4627 y(s)1775 4607 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1878 4573 a Fy(\016)1878 4627 y(s)1915 4607 y FB(q)p FE(d)p FD(s;)14 b(\034)2105 4619 y FG(1)2143 4514 y Fr(\011)2192 4532 y Fy(T)2244 4607 y FD(;)637 b FE(\(5.2\))0 4857 y(whose)27 b(empirical)c(mean)j (and)i(co)n(v)-5 b(ariance)24 b(are)j(denoted)g(b)n(y)p 0 TeXcolorgray 1959 4835 a(^)1957 4857 y Fh(\030)2001 4798 y Fx(p)p Fy(M)6 b Fx(q)p 0 TeXcolorgray 2155 4857 a FE(and)p 0 TeXcolorgray 2330 4836 a(^)2316 4857 y FJ(C)2385 4827 y Fx(p)p Fy(M)g Fx(q)p 0 TeXcolorgray 2538 4857 a FE(resp)r(ectiv)n(ely:)p 0 TeXcolorgray 404 5092 a SDict begin H.S end 404 5092 a 404 5092 a SDict begin 12 H.A end 404 5092 a 404 5092 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.3) cvn /DEST pdfmark end 404 5092 a 0 TeXcolorgray 406 5071 a FE(^)404 5092 y Fh(\030)p 0 TeXcolorgray 449 5058 a Fx(p)p Fy(M)g Fx(q)597 5092 y FB(\020)719 5036 y FE(1)p 695 5073 90 4 v 695 5149 a FD(M)827 4993 y Fy(M)816 5014 y Fr(\270)808 5186 y Fy(i)p Fx(\020)p FG(1)930 5092 y Fh(\030)974 5055 y Fx(p)p Fy(i)p Fx(q)1054 5092 y FD(;)1188 5071 y FE(^)1174 5092 y FJ(C)1243 5058 y Fx(p)p Fy(M)g Fx(q)1391 5092 y FB(\020)1513 5036 y FE(1)p 1489 5073 V 1489 5149 a FD(M)1621 4993 y Fy(M)1610 5014 y Fr(\270)1602 5186 y Fy(i)p Fx(\020)p FG(1)1724 5092 y Fh(\030)1768 5055 y Fx(p)p Fy(i)p Fx(q)1848 5092 y FB(p)p Fh(\030)1925 5055 y Fx(p)p Fy(i)p Fx(q)2004 5092 y FB(q)2036 5058 y Fy(T)2108 5092 y FB(\001)2192 5071 y FE(^)2191 5092 y Fh(\030)2235 5033 y Fx(p)p Fy(M)g Fx(q)2361 5092 y FB(p)2395 5071 y FE(^)2393 5092 y Fh(\030)2438 5033 y Fx(p)p Fy(M)g Fx(q)2563 5092 y FB(q)2595 5058 y Fy(T)2648 5092 y FD(:)233 b FE(\(5.3\))p 0 TeXcolorgray 0 TeXcolorgray eop end end %%Page: 15 15 TeXDict begin HPSdict begin 15 14 bop 0 TeXcolorgray 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a 0 TeXcolorgray -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.15) cvn /DEST pdfmark end -8 -8 a 0 TeXcolorgray 0 TeXcolorgray 1050 83 a FI(Dry)23 b(friction)i(problem)f(with)h(noise)968 b FE(15)p 0 TeXcolorgray 0 TeXcolorgray 28 286 a(F)-7 b(rom)26 b(the)i(cen)n(tral)d(limit)g(theorem,)h(w)n(e)h(ha)n(v)n(e)g (the)h(con)n(v)n(ergence)d(in)i(distribution)d(of)p 0 TeXcolorgray 2770 264 a(^)2768 286 y Fh(\030)p 0 TeXcolorgray 2813 256 a Fx(p)p Fy(M)6 b Fx(q)2938 286 y FE(:)p 0 TeXcolorgray 855 504 a SDict begin H.S end 855 504 a 855 504 a SDict begin 12 H.A end 855 504 a 855 504 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.4) cvn /DEST pdfmark end 855 504 a -75 x FB(?)p 924 429 90 3 v 75 x FD(M)1014 436 y Fr(\000)1054 482 y FE(^)1052 504 y Fh(\030)1097 445 y Fx(p)p Fy(M)g Fx(q)1241 504 y FB(\001)18 b FA(E)8 b FB(r)p Fh(\030)g FB(s)1481 436 y Fr(\010)1542 459 y Fy(M)e Fx(\321\0008)1597 504 y FB(\335)-14 b(\321)77 b Fe(N)1888 436 y Fr(\000)1927 504 y FJ(0)1975 519 y Ff(R)2022 502 y Fq(2)2053 504 y FD(;)14 b FJ(C)2159 436 y Fr(\010)2197 504 y FD(;)684 b FE(\(5.4\))0 709 y(where)27 b FJ(C)c FB(\020)g FA(E)8 b FB(r)p Fh(\030)g(\030)593 672 y Fy(T)645 709 y FB(s)18 b(\001)g FA(E)9 b FB(r)p Fh(\030)f FB(s)p FA(E)g FB(r)p Fh(\030)g FB(s)1090 679 y Fy(T)1142 709 y FE(.)p 0 TeXcolorgray 37 w(By)27 b(the)h(delta)f(metho)r(d,)g(w)n(e)g (get)0 972 y SDict begin H.S end 0 972 a 0 972 a SDict begin 12 H.A end 0 972 a 0 972 a SDict begin [/View [/XYZ H.V]/Dest 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Fx(p)p Fy(M)6 b Fx(q)p 0 TeXcolorgray 196 1428 a Fr(\001)p 0 TeXcolorgray 264 1443 a FE(^)255 1465 y FD(\030)295 1422 y Fx(p)p Fy(M)g Fx(q)291 1487 y FG(1)p 0 TeXcolorgray 255 1502 166 4 v 0 TeXcolorgray 264 1578 a FE(^)255 1600 y FD(\030)295 1556 y Fx(p)p Fy(M)g Fx(q)291 1622 y FG(2)p 0 TeXcolorgray 431 1521 a FB(\001)506 1465 y FA(E)i FB(r)p 0 TeXcolorgray FD(\030)620 1477 y FG(1)p 0 TeXcolorgray 663 1465 a FB(s)p 506 1502 187 4 v 506 1578 a FA(E)g FB(r)p 0 TeXcolorgray FD(\030)620 1590 y FG(2)p 0 TeXcolorgray 663 1578 a FB(s)702 1428 y Fr(\011)p 0 TeXcolorgray 774 1476 a Fy(M)p 0 TeXcolorgray 7 w Fx(\321\0008)829 1521 y FB(\335)-14 b(\321)78 b Fe(N)12 b FB(p)p FE(0)p FD(;)i FE(1)p FB(q)p FD(;)179 b FB(p)t FE(^)-46 b FD(\033)p 0 TeXcolorgray 1590 1487 a Fy(M)p 0 TeXcolorgray 1665 1521 a FB(q)1697 1487 y FG(2)1757 1521 y FB(\020)1845 1379 y Fr(\003)2056 1471 y FE(1)p FB({)p 0 TeXcolorgray 2143 1449 a FE(^)2134 1471 y FD(\030)2174 1428 y Fx(p)p Fy(M)6 b Fx(q)2170 1493 y FG(2)p 0 TeXcolorgray 1911 1588 a FB(\001)p 0 TeXcolorgray 1985 1566 a FE(^)1976 1588 y FD(\030)2016 1545 y Fx(p)p Fy(M)g Fx(q)2012 1610 y FG(1)p 0 TeXcolorgray 2141 1588 a FB({p)p 0 TeXcolorgray 2218 1566 a FE(^)2209 1588 y FD(\030)2249 1545 y Fx(p)p Fy(M)g Fx(q)2245 1610 y FG(2)p 0 TeXcolorgray 2374 1588 a FB(q)2406 1558 y FG(2)2444 1379 y Fr(\013)2510 1397 y Fy(T)2589 1500 y FE(^)2576 1521 y FJ(C)p 0 TeXcolorgray 12 x Fy(M)p 0 TeXcolorgray 2732 1379 a Fr(\003)2943 1471 y FE(1)p FB({)p 0 TeXcolorgray 3030 1449 a FE(^)3021 1471 y FD(\030)3061 1428 y Fx(p)p Fy(M)g Fx(q)3057 1493 y FG(2)p 0 TeXcolorgray 2798 1588 a FB(\001)p 0 TeXcolorgray 2872 1566 a FE(^)2863 1588 y FD(\030)2903 1545 y Fx(p)p Fy(M)g Fx(q)2899 1610 y FG(1)p 0 TeXcolorgray 3028 1588 a FB({p)p 0 TeXcolorgray 3105 1566 a FE(^)3096 1588 y FD(\030)3136 1545 y Fx(p)p Fy(M)g Fx(q)3132 1610 y FG(2)p 0 TeXcolorgray 3262 1588 a FB(q)3294 1558 y FG(2)3331 1379 y Fr(\013)3411 1521 y FD(:)2904 1696 y FE(\(5.6\))0 1795 y(W)-7 b(e)29 b(can)f(deduce)h(from)e(this)h(con)n(v)n(ergence)f (in)g(distribution)f(an)j(asymptotic)d(95)h(\045)i(con\014dence)0 1895 y(in)n(terv)-5 b(al)25 b(for)i FA(E)8 b FB(r)p 0 TeXcolorgray FD(\030)541 1907 y FG(1)p 0 TeXcolorgray 585 1895 a FB(s{)p FA(E)f FB(r)p 0 TeXcolorgray FD(\030)763 1907 y FG(2)p 0 TeXcolorgray 806 1895 a FB(s)27 b FE(\(whic)n(h)g(is)g (the)h(quan)n(tit)n(y)e(of)h(in)n(terest)g(b)n(y)g(\()p 0 0.6 0 TeXcolorrgb 2231 1895 a SDict begin H.S end 2231 1895 a 0 0.6 0 TeXcolorrgb FE(4.1)p 0 0.6 0 TeXcolorrgb 2338 1842 a SDict begin H.R end 2338 1842 a 2338 1895 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 0]BorderArrayPatch/Subtype /Link/Dest (equation.4.1) cvn H.B /ANN pdfmark end 2338 1895 a 0 TeXcolorgray FE(\)\):)105 2160 y SDict begin H.S end 105 2160 a 105 2160 a SDict begin 12 H.A end 105 2160 a 105 2160 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.7) cvn /DEST pdfmark end 105 2160 a FA(P)171 2017 y Fr(\003)245 2104 y FA(E)8 b FB(r)p 0 TeXcolorgray FD(\030)359 2116 y FG(1)p 0 TeXcolorgray 402 2104 a FB(s)p 245 2141 187 4 v 245 2217 a FA(E)g FB(r)p 0 TeXcolorgray FD(\030)359 2229 y FG(2)p 0 TeXcolorgray 402 2217 a FB(s)464 2160 y(P)531 2067 y Fr(\001)p 0 TeXcolorgray 599 2082 a FE(^)590 2104 y FD(\030)630 2061 y Fx(p)p Fy(M)e Fx(q)626 2126 y FG(1)p 0 TeXcolorgray 590 2141 166 4 v 0 TeXcolorgray 599 2216 a FE(^)590 2238 y FD(\030)630 2195 y Fx(p)p Fy(M)g Fx(q)626 2260 y FG(2)p 0 TeXcolorgray 785 2160 a FB(\001)18 b FE(1)p FD(:)p FE(96)t(^)-46 b FD(\033)p 0 TeXcolorgray 1067 2126 a Fx(p)p Fy(M)6 b Fx(q)p 0 TeXcolorgray 0 TeXcolorgray 1191 2160 a FD(M)p 0 TeXcolorgray 1281 2126 a Fx(\001)1342 2103 y Fq(1)p 1342 2112 29 3 v 1342 2146 a(2)1384 2160 y FD(;)p 0 TeXcolorgray 1440 2082 a FE(^)1431 2104 y FD(\030)1471 2061 y Fx(p)p Fy(M)g Fx(q)1467 2126 y FG(1)p 0 TeXcolorgray 1431 2141 166 4 v 0 TeXcolorgray 1440 2216 a FE(^)1431 2238 y FD(\030)1471 2195 y Fx(p)p Fy(M)g Fx(q)1467 2260 y FG(2)p 0 TeXcolorgray 1625 2160 a FB(\000)18 b FE(1)p FD(:)p FE(96)t(^)-46 b FD(\033)p 0 TeXcolorgray 1907 2126 a Fx(p)p Fy(M)6 b Fx(q)p 0 TeXcolorgray 0 TeXcolorgray 2032 2160 a FD(M)p 0 TeXcolorgray 2121 2126 a Fx(\001)2182 2103 y Fq(1)p 2182 2112 29 3 v 2182 2146 a(2)2224 2067 y Fr(\011)2274 2017 y(\013)p 0 TeXcolorgray 2363 2114 a Fy(M)p 0 TeXcolorgray 6 w Fx(\321\0008)2418 2160 y FB(\335)-14 b(\321)77 b FE(0)p FD(:)p FE(95)p FD(:)103 b FE(\(5.7\))150 2424 y(Note)28 b(that)p 0 TeXcolorgray 557 2655 a FD(\030)593 2667 y FG(1)p 0 TeXcolorgray 653 2655 a FB(\020)851 2576 y Fr(\270)732 2749 y FG(0)p Fx(\244)p Fy(i)p Fx(\244)p Fy(i)913 2757 y Fp(\034)941 2769 y Fq(1)979 2749 y Fx(\001)p FG(1)1076 2542 y Fr(\273)1139 2562 y Fy(T)1178 2570 y Fp(i)p Fd(\000)p Fq(1)1118 2730 y Fy(T)1157 2738 y Fp(i)1293 2655 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1450 2620 a Fy(\016)1450 2675 y(T)1489 2683 y Fp(i)1520 2655 y FD(;)14 b FE(\010)p 0 TeXcolorgray 20 x Fy(X)p 0 TeXcolorgray 1676 2655 a Fp(\016)1676 2695 y(T)1711 2708 y(i)1741 2675 y Fy(;)p 0 TeXcolorgray(Y)p 0 TeXcolorgray 1814 2655 a Fp(\016)1814 2695 y(T)1849 2708 y(i)1883 2655 y FB(p)p FD(s)19 b FB(\001)f FD(T)2105 2667 y Fy(i)2132 2655 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 2236 2620 a Fy(\016)2236 2675 y(T)2275 2683 y Fp(i)2305 2655 y FB(qq)p FE(d)q FD(s)736 2928 y FB(\000)819 2815 y Fr(\273)882 2836 y Fy(\034)913 2844 y Fq(1)861 3004 y Fy(T)900 3012 y Fp(i)922 3020 y(\034)950 3032 y Fq(1)1009 2928 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1166 2894 a Fy(\016)1166 2949 y(T)1205 2957 y Fp(i)1227 2965 y(\034)1255 2977 y Fq(1)1301 2928 y FD(;)14 b FE(\010)p 0 TeXcolorgray 21 x Fy(X)p 0 TeXcolorgray 1457 2929 a Fp(\016)1457 2968 y(T)1492 2981 y(i)1514 2989 y(\034)1542 3001 y Fq(1)1587 2949 y Fy(;)p 0 TeXcolorgray(Y)p 0 TeXcolorgray 1660 2929 a Fp(\016)1660 2968 y(T)1695 2981 y(i)1717 2989 y(\034)1745 3001 y Fq(1)1794 2928 y FB(p)p FD(s)k FB(\001)g FD(T)2015 2940 y Fy(i)2038 2948 y Fp(\034)2066 2960 y Fq(1)2107 2928 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 2211 2894 a Fy(\016)2211 2949 y(T)2250 2957 y Fp(i)2272 2965 y(\034)2300 2977 y Fq(1)2346 2928 y FB(qq)p FE(d)p FD(s;)2904 2928 y SDict begin H.S end 2904 2928 a 2904 2928 a SDict begin 15 H.A end 2904 2928 a 2904 2928 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.8) cvn /DEST pdfmark end 2904 2928 a FE(\(5.8\))0 3194 y(where)37 b FD(i)279 3206 y Fy(\034)310 3214 y Fq(1)385 3194 y FB(\020)i FE(max)o FB(t)p FD(i;)f(T)820 3206 y Fy(i)887 3194 y FB(\244)h FD(\034)1027 3206 y FG(1)1065 3194 y FB(u)p FD(:)e FE(If)h FD(f)46 b FE(do)r(es)37 b(not)h(dep)r(end)g(on)f FD(v)k FE(then)d(the)g(form)n(ula)c(ab)r(o)n (v)n(e)0 3294 y(b)r(ecomes)26 b(simple)252 3413 y Fr(\273)314 3434 y Fy(\034)345 3442 y Fq(1)294 3602 y FG(0)395 3526 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 553 3492 a Fy(\016)553 3547 y(s)589 3526 y FB(q)p FE(d)p FD(s)23 b FB(\020)936 3447 y Fr(\270)817 3620 y FG(0)p Fx(\244)p Fy(i)p Fx(\244)p Fy(i)998 3628 y Fp(\034)1026 3640 y Fq(1)1064 3620 y Fx(\001)p FG(1)1162 3526 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1319 3492 a Fy(\016)1319 3547 y(T)1358 3555 y Fp(i)1389 3526 y FB(qp)p FD(T)1502 3538 y Fy(i)p Fx(\000)p FG(1)1632 3526 y FB(\001)18 b FD(T)1764 3538 y Fy(i)1791 3526 y FB(q)h(\000)f FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 2082 3492 a Fy(\016)2082 3547 y(T)2121 3555 y Fp(i)2143 3563 y(\034)2171 3575 y Fq(1)2216 3526 y FB(qp)p FD(\034)2316 3538 y FG(1)2373 3526 y FB(\001)18 b FD(T)2505 3538 y Fy(i)2528 3546 y Fp(\034)2556 3558 y Fq(1)2597 3526 y FB(q)p FD(:)2904 3526 y SDict begin H.S end 2904 3526 a 2904 3526 a SDict begin 15 H.A end 2904 3526 a 2904 3526 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.9) cvn /DEST pdfmark end 2904 3526 a FE(\(5.9\))0 3810 y(With)30 b(the)h(particular)d(c)n(hoice)h(of)h FD(f)9 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)14 b(v)s FB(q)29 b(\020)f FJ(1)1508 3826 y Fx(t)1537 3825 y Fy(v)r Fx(\020)p FG(0)p Fy(;)15 b Fx(|)p 0 TeXcolorgray Fy(x)p 0 TeXcolorgray -1 w Fx(|\244)p Fy(\026)1857 3833 y Fq(s)1884 3825 y Fx(u)1918 3810 y FE(,)32 b(the)f(form)n(ula)c(remains)h(simple)g(as)0 3910 y(w)n(ell)62 4013 y Fr(\273)124 4033 y Fy(\034)155 4041 y Fq(1)103 4202 y FG(0)205 4126 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 362 4092 a Fy(\016)362 4146 y(s)398 4126 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 502 4092 a Fy(\016)502 4146 y(s)539 4126 y FB(q)p FE(d)p FD(s)23 b FB(\020)886 4047 y Fr(\270)767 4220 y FG(0)p Fx(\244)p Fy(i)p Fx(\244)p Fy(i)948 4228 y Fp(\034)976 4240 y Fq(1)1013 4220 y Fx(\001)p FG(1)1111 4126 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 1268 4092 a Fy(\016)1268 4146 y(T)1307 4154 y Fp(i)1338 4126 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1442 4092 a Fy(\016)1442 4146 y(T)1481 4154 y Fp(i)1512 4126 y FB(qp)p FD(T)1625 4138 y Fy(i)p Fx(\000)p FG(1)1755 4126 y FB(\001)18 b FD(T)1887 4138 y Fy(i)1914 4126 y FB(q)h(\000)f FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 2205 4092 a Fy(\016)2205 4146 y(T)2244 4154 y Fp(i)2266 4162 y(\034)2294 4174 y Fq(1)2339 4126 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 2443 4092 a Fy(\016)2443 4146 y(T)2482 4154 y Fp(i)2504 4162 y(\034)2532 4174 y Fq(1)2578 4126 y FB(qp)p FD(\034)2678 4138 y FG(1)2734 4126 y FB(\001)18 b FD(T)2866 4138 y Fy(i)2889 4146 y Fp(\034)2917 4158 y Fq(1)2958 4126 y FB(q)p FD(:)2863 4327 y SDict begin H.S end 2863 4327 a 2863 4327 a SDict begin 15 H.A end 2863 4327 a 2863 4327 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.10) cvn /DEST pdfmark end 2863 4327 a FE(\(5.10\))0 4523 y(When)28 b FD(f)9 b FB(p)p 0 TeXcolorgray FD(x)p 0 TeXcolorgray(;)14 b(v)s FB(q)24 b(\020)f FD(v)638 4493 y FG(2)703 4523 y FE(then)28 b(it)f(b)r(ecomes)f(sligh)n(tly)e(more)i(complicated)106 4662 y Fr(\273)168 4682 y Fy(\034)199 4690 y Fq(1)148 4850 y FG(0)249 4775 y FD(f)9 b FB(p)p 0 TeXcolorgray FD(X)p 0 TeXcolorgray 407 4740 a Fy(\016)407 4795 y(s)443 4775 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 547 4740 a Fy(\016)547 4795 y(s)583 4775 y FB(q)p FE(d)q FD(s)23 b FB(\020)921 4696 y Fr(\270)802 4869 y FG(0)p Fx(\244)p Fy(i)p Fx(\244)p Fy(i)983 4877 y Fp(\034)1011 4889 y Fq(1)1049 4869 y Fx(\001)p FG(1)1147 4662 y Fr(\273)1209 4682 y Fy(T)1248 4690 y Fp(i)p Fd(\000)p Fq(1)1188 4850 y Fy(T)1227 4858 y Fp(i)1363 4707 y Fr(\000)1401 4775 y FE(\010)p 0 TeXcolorgray 20 x Fy(X)p 0 TeXcolorgray 1520 4775 a Fp(\016)1520 4815 y(T)1555 4828 y(i)1585 4795 y Fy(;)p 0 TeXcolorgray(Y)p 0 TeXcolorgray 1658 4775 a Fp(\016)1658 4815 y(T)1693 4828 y(i)1728 4775 y FB(p)p FD(s)18 b FB(\001)g FD(T)1949 4787 y Fy(i)1976 4775 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 2080 4740 a Fy(\016)2080 4795 y(T)2119 4803 y Fp(i)2150 4775 y FB(q)2182 4707 y Fr(\010)2220 4725 y FG(2)2257 4775 y FE(d)p FD(s)p FJ(1)2390 4795 y Fx(t|)p 0 TeXcolorgray Fy(X)p 0 TeXcolorgray 2497 4775 a Fp(\016)2497 4815 y(T)2532 4828 y(i)2562 4795 y Fx(|\020)p FG(1)p Fx(u)807 5048 y FB(\000)890 4935 y Fr(\273)952 4956 y Fy(\034)983 4964 y Fq(1)931 5124 y Fy(T)970 5132 y Fp(i)992 5140 y(\034)1020 5152 y Fq(1)1079 4980 y Fr(\000)1118 5048 y FE(\010)p 0 TeXcolorgray 21 x Fy(X)p 0 TeXcolorgray 1236 5049 a Fp(\016)1236 5088 y(T)1271 5101 y(i)1293 5109 y(\034)1321 5121 y Fq(1)1366 5069 y Fy(;)p 0 TeXcolorgray(Y)p 0 TeXcolorgray 1439 5049 a Fp(\016)1439 5088 y(T)1474 5101 y(i)1496 5109 y(\034)1524 5121 y Fq(1)1573 5048 y FB(p)p FD(s)h FB(\001)f FD(T)1795 5060 y Fy(i)1818 5068 y Fp(\034)1846 5080 y Fq(1)1887 5048 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1991 5014 a Fy(\016)1991 5069 y(T)2030 5077 y Fp(i)2052 5085 y(\034)2080 5097 y Fq(1)2125 5048 y FB(q)2157 4980 y Fr(\010)2196 4998 y FG(2)2233 5048 y FE(d)p FD(s)p FJ(1)2366 5069 y Fx(t|)p 0 TeXcolorgray Fy(Y)p 0 TeXcolorgray 2467 5049 a Fp(\016)2467 5088 y(T)2502 5101 y(i)2524 5109 y(\034)2552 5121 y Fq(1)2597 5069 y Fx(|\020)p FG(1)p Fx(u)2734 5048 y FD(:)2863 5048 y SDict begin H.S end 2863 5048 a 2863 5048 a SDict begin 15 H.A end 2863 5048 a 2863 5048 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.11) cvn /DEST pdfmark end 2863 5048 a FE(\(5.11\))p 0 TeXcolorgray 0 TeXcolorgray eop end end %%Page: 16 16 TeXDict begin HPSdict begin 16 15 bop 0 TeXcolorgray 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a 0 TeXcolorgray -8 -8 a SDict begin H.S end -8 -8 a -8 -8 a SDict begin H.R end -8 -8 a -8 -8 a SDict begin [/View [/XYZ H.V]/Dest (page.16) cvn /DEST pdfmark end -8 -8 a 0 TeXcolorgray 0 TeXcolorgray 0 83 a FE(16)965 b FI(J.)23 b(Garnier,)h(Z.)f(Lu,)h(and)g(L.)f(Mertz)p 0 TeXcolorgray 0 286 a FE(If)p 0 TeXcolorgray 74 w Fs(b)p FB(p)p FD(v)s FB(q)39 b(\020)f(\001)p FD(v)p 0 TeXcolorgray 3 w FE(,)h(then)e(eac)n(h)f(of)h(the)g(in)n(tegrals)c(in)j(the)h(righ)n (t-hand)e(side)g(can)i(b)r(e)g(computed)0 386 y(explicitly:)266 475 y Fr(\273)328 496 y 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FB(p)p FD(T)1195 831 y Fy(i)1218 839 y Fp(\034)1246 851 y Fq(1)1287 819 y FD(;)c(\034)1360 831 y FG(1)1397 819 y FE(;)p 0 TeXcolorgray 14 w FD(X)p 0 TeXcolorgray 1510 785 a Fy(\016)1510 840 y(T)1549 848 y Fp(i)1571 856 y(\034)1599 868 y Fq(1)1644 819 y FD(;)p 0 TeXcolorgray 14 w(Y)p 0 TeXcolorgray 1748 785 a Fy(\016)1748 840 y(T)1787 848 y Fp(i)1809 856 y(\034)1837 868 y Fq(1)1882 819 y FD(;)p 0 TeXcolorgray 14 w(V)p 0 TeXcolorgray 1986 785 a Fy(\016)1986 840 y(T)2025 848 y Fp(i)2047 856 y(\034)2075 868 y Fq(1)2120 819 y FB(q)p FJ(1)2200 839 y Fx(t|)p 0 TeXcolorgray Fy(X)p 0 TeXcolorgray 2308 819 a Fp(\016)2308 859 y(T)2343 872 y(i)2365 880 y(\034)2393 892 y Fq(1)2438 839 y Fx(|\020)p FG(1)p Fx(u)2574 819 y FD(;)2863 819 y SDict begin H.S end 2863 819 a 2863 819 a SDict begin 15 H.A end 2863 819 a 2863 819 a SDict begin [/View [/XYZ H.V]/Dest (equation.5.12) cvn /DEST pdfmark end 2863 819 a FE(\(5.12\))0 1041 y(with)30 b(\011)p FB(p)p FD(\022)r(;)14 b(\022)408 1011 y Fx(1)430 1041 y 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[1.0 0.0 0.0 1.0 -199.21013 -11.62952 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FE(2)2507 1847 y Fx(\001)p FG(4)2465 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -151.35326 -11.62952 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FE(2)2507 1847 y Fx(\001)p FG(3)2465 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -103.4964 -11.62952 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FE(2)2507 1847 y Fx(\001)p FG(2)2465 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -55.63954 -11.62952 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FE(2)2507 1847 y Fx(\001)p FG(1)2465 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -258.3881 -3.2102 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FE(0)p FD(:)p FE(1)2465 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -258.3881 29.06813 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FE(0)p FD(:)p FE(2)2465 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -258.3881 61.3465 ] concat pgfs 2465 1877 a 0 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pgfsc pgfstr grestore newpath -191.45737 137.31763 moveto -189.73177 134.3288 lineto -193.18298 134.3288 lineto closepath gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath -239.3208 136.83992 moveto -237.5952 133.85109 lineto -241.0464 133.85109 lineto closepath gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath pgfstr restore save save [1.0 0.0 0.0 1.0 -147.40358 -25.38849 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FD(\016)2465 1877 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -266.72289 69.22932 ] concat pgfs 2465 1877 a 0 setgray 2465 1877 a FD(P)2518 1889 y FG(stic)n(k)2465 1877 y pgfr restore restore restore newpath restore pgfc 158 2116 a pgfr restore save restore save restore restore newpath restore pgfc 1177 2116 a 1177 2116 a 1177 2116 a pgfo save 0 setgray 0.3985 pgfw save save restore save restore save [0.49 0.0 0.0 0.49 0.0 0.0 ] concat pgfs 1177 2116 a pgfr restore save restore save restore save restore save restore save [0.49 0.0 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moveto -237.89099 35.08571 lineto -242.13806 85.20815 moveto -237.89099 85.20815 lineto -242.13806 135.33058 moveto -237.89099 135.33058 lineto -47.86415 35.08571 moveto -52.11122 35.08571 lineto -47.86415 85.20815 moveto -52.11122 85.20815 lineto -47.86415 135.33058 moveto -52.11122 135.33058 lineto pgfstr 0 TeXcolorgray restore restore -242.13806 0.0 moveto -242.13806 161.39426 lineto -47.86415 161.39426 lineto -47.86415 0.0 lineto -242.13806 0.0 lineto closepath pgfstr save save [1.0 0.0 0.0 1.0 -247.06699 -11.62952 ] concat pgfs 3506 1877 a 0 setgray 3506 1877 a FE(2)3548 1847 y Fx(\001)p FG(5)3506 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -199.21013 -11.62952 ] concat pgfs 3506 1877 a 0 setgray 3506 1877 a FE(2)3548 1847 y Fx(\001)p FG(4)3506 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -151.35326 -11.62952 ] concat pgfs 3506 1877 a 0 setgray 3506 1877 a FE(2)3548 1847 y Fx(\001)p FG(3)3506 1877 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -103.4964 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165.42139 145.871 lineto 166.81053 145.871 lineto 168.19968 145.871 lineto 169.58884 145.871 lineto 170.978 145.871 lineto 172.36716 145.871 lineto 173.75632 145.871 lineto 175.14546 145.871 lineto 176.53462 145.871 lineto 177.92378 145.871 lineto 179.31294 145.871 lineto 180.70209 145.871 lineto 182.09125 145.871 lineto 183.48041 145.871 lineto 184.86957 145.871 lineto 186.25873 145.871 lineto 187.64787 145.871 lineto 189.03702 145.871 lineto 190.42618 145.871 lineto 191.81534 145.871 lineto 193.20448 145.871 lineto 194.59364 145.871 lineto 195.9828 145.871 lineto 197.37196 145.871 lineto pgfstr restore save 0 setgray 22.01154 73.01236 moveto 44.0291 75.08745 lineto 66.04367 75.16429 lineto 88.05653 74.85687 lineto 110.07077 74.54945 lineto 132.08533 74.39574 lineto 154.10225 74.3189 lineto 176.11679 74.24203 lineto 198.1317 74.24203 lineto 220.14626 74.24203 lineto 242.16081 74.24203 lineto 264.17471 74.24203 lineto 286.18925 74.24203 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 74.70317 moveto 165.42139 74.70317 lineto 166.81053 74.70317 lineto 168.19968 74.70317 lineto 169.58884 74.70317 lineto 170.978 74.70317 lineto 172.36716 74.70317 lineto 173.75632 74.70317 lineto 175.14546 74.70317 lineto 176.53462 74.70317 lineto 177.92378 74.70317 lineto 179.31294 74.70317 lineto 180.70209 74.70317 lineto 182.09125 74.70317 lineto 183.48041 74.70317 lineto 184.86957 74.70317 lineto 186.25873 74.70317 lineto 187.64787 74.70317 lineto 189.03702 74.70317 lineto 190.42618 74.70317 lineto 191.81534 74.70317 lineto 193.20448 74.70317 lineto 194.59364 74.70317 lineto 195.9828 74.70317 lineto 197.37196 74.70317 lineto pgfstr restore save 0 setgray 22.01154 36.81358 moveto 44.0291 40.57948 lineto 66.04367 42.19345 lineto 88.05653 42.88513 lineto 110.07077 43.1157 lineto 132.08533 43.26941 lineto 154.10225 43.34627 lineto 176.11679 43.34627 lineto 198.1317 43.42314 lineto 220.14626 43.42314 lineto 242.16081 43.42314 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 43.42314 moveto 165.42139 43.42314 lineto 166.81053 43.42314 lineto 168.19968 43.42314 lineto 169.58884 43.42314 lineto 170.978 43.42314 lineto 172.36716 43.42314 lineto 173.75632 43.42314 lineto 175.14546 43.42314 lineto 176.53462 43.42314 lineto 177.92378 43.42314 lineto 179.31294 43.42314 lineto 180.70209 43.42314 lineto 182.09125 43.42314 lineto 183.48041 43.42314 lineto 184.86957 43.42314 lineto 186.25873 43.42314 lineto 187.64787 43.42314 lineto 189.03702 43.42314 lineto 190.42618 43.42314 lineto 191.81534 43.42314 lineto 193.20448 43.42314 lineto 194.59364 43.42314 lineto 195.9828 43.42314 lineto 197.37196 43.42314 lineto pgfstr restore save 0 setgray 22.01154 20.05917 moveto 44.0291 24.59363 lineto 66.04367 26.89929 lineto 88.05653 28.05211 lineto 110.07077 28.66695 lineto 132.08533 28.8975 lineto 154.10225 29.05122 lineto 176.11679 29.12808 lineto 198.1317 29.12808 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 29.20494 moveto 165.42139 29.20494 lineto 166.81053 29.20494 lineto 168.19968 29.20494 lineto 169.58884 29.20494 lineto 170.978 29.20494 lineto 172.36716 29.20494 lineto 173.75632 29.20494 lineto 175.14546 29.20494 lineto 176.53462 29.20494 lineto 177.92378 29.20494 lineto 179.31294 29.20494 lineto 180.70209 29.20494 lineto 182.09125 29.20494 lineto 183.48041 29.20494 lineto 184.86957 29.20494 lineto 186.25873 29.20494 lineto 187.64787 29.20494 lineto 189.03702 29.20494 lineto 190.42618 29.20494 lineto 191.81534 29.20494 lineto 193.20448 29.20494 lineto 194.59364 29.20494 lineto 195.9828 29.20494 lineto 197.37196 29.20494 lineto pgfstr restore save 0 setgray 22.01154 12.06624 moveto 44.0291 16.98497 lineto 66.04367 19.6749 lineto 88.05653 20.98143 lineto 110.07077 21.67313 lineto 132.08533 22.0574 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 23.21024 moveto 165.42139 23.21024 lineto 166.81053 23.21024 lineto 168.19968 23.21024 lineto 169.58884 23.21024 lineto 170.978 23.21024 lineto 172.36716 23.21024 lineto 173.75632 23.21024 lineto 175.14546 23.21024 lineto 176.53462 23.21024 lineto 177.92378 23.21024 lineto 179.31294 23.21024 lineto 180.70209 23.21024 lineto 182.09125 23.21024 lineto 183.48041 23.21024 lineto 184.86957 23.21024 lineto 186.25873 23.21024 lineto 187.64787 23.21024 lineto 189.03702 23.21024 lineto 190.42618 23.21024 lineto 191.81534 23.21024 lineto 193.20448 23.21024 lineto 194.59364 23.21024 lineto 195.9828 23.21024 lineto 197.37196 23.21024 lineto pgfstr restore save 0 setgray 22.01154 8.14662 moveto 44.0291 13.29591 lineto 66.04367 16.06271 lineto 88.05653 17.59981 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 19.8286 moveto 165.42139 19.8286 lineto 166.81053 19.8286 lineto 168.19968 19.8286 lineto 169.58884 19.8286 lineto 170.978 19.8286 lineto 172.36716 19.8286 lineto 173.75632 19.8286 lineto 175.14546 19.8286 lineto 176.53462 19.8286 lineto 177.92378 19.8286 lineto 179.31294 19.8286 lineto 180.70209 19.8286 lineto 182.09125 19.8286 lineto 183.48041 19.8286 lineto 184.86957 19.8286 lineto 186.25873 19.8286 lineto 187.64787 19.8286 lineto 189.03702 19.8286 lineto 190.42618 19.8286 lineto 191.81534 19.8286 lineto 193.20448 19.8286 lineto 194.59364 19.8286 lineto 195.9828 19.8286 lineto 197.37196 19.8286 lineto pgfstr restore restore save 0 setgray 0 setgray 22.01154 152.24713 moveto 22.87433 150.75272 lineto 21.14873 150.75272 lineto closepath pgfstr 44.0291 153.01569 moveto 44.8919 151.52127 lineto 43.1663 151.52127 lineto closepath pgfstr 66.04367 151.24803 moveto 66.90646 149.75362 lineto 65.18086 149.75362 lineto closepath pgfstr 88.05653 149.32666 moveto 88.91934 147.83224 lineto 87.19374 147.83224 lineto closepath pgfstr 110.07077 148.09697 moveto 110.93358 146.60255 lineto 109.20796 146.60255 lineto closepath pgfstr 132.08533 147.32841 moveto 132.94814 145.834 lineto 131.22253 145.834 lineto closepath pgfstr 154.10225 146.94414 moveto 154.96506 145.44972 lineto 153.23944 145.44972 lineto closepath pgfstr 176.11679 146.71358 moveto 176.9796 145.21916 lineto 175.254 145.21916 lineto closepath pgfstr 198.1317 146.55986 moveto 198.99449 145.06544 lineto 197.26889 145.06544 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 22.01154 74.00864 moveto 22.87433 72.51422 lineto 21.14873 72.51422 lineto closepath pgfstr 44.0291 76.08372 moveto 44.8919 74.58931 lineto 43.1663 74.58931 lineto closepath pgfstr 66.04367 76.16057 moveto 66.90646 74.66615 lineto 65.18086 74.66615 lineto closepath pgfstr 88.05653 75.85315 moveto 88.91934 74.35873 lineto 87.19374 74.35873 lineto closepath pgfstr 110.07077 75.54573 moveto 110.93358 74.05132 lineto 109.20796 74.05132 lineto closepath pgfstr 132.08533 75.39201 moveto 132.94814 73.8976 lineto 131.22253 73.8976 lineto closepath pgfstr 154.10225 75.31517 moveto 154.96506 73.82076 lineto 153.23944 73.82076 lineto closepath pgfstr 176.11679 75.23831 moveto 176.9796 73.7439 lineto 175.254 73.7439 lineto closepath pgfstr 198.1317 75.23831 moveto 198.99449 73.7439 lineto 197.26889 73.7439 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 22.01154 37.80986 moveto 22.87433 36.31544 lineto 21.14873 36.31544 lineto closepath pgfstr 44.0291 41.57576 moveto 44.8919 40.08134 lineto 43.1663 40.08134 lineto closepath pgfstr 66.04367 43.18973 moveto 66.90646 41.69531 lineto 65.18086 41.69531 lineto closepath pgfstr 88.05653 43.88141 moveto 88.91934 42.387 lineto 87.19374 42.387 lineto closepath pgfstr 110.07077 44.11198 moveto 110.93358 42.61757 lineto 109.20796 42.61757 lineto closepath pgfstr 132.08533 44.26569 moveto 132.94814 42.77127 lineto 131.22253 42.77127 lineto closepath pgfstr 154.10225 44.34254 moveto 154.96506 42.84813 lineto 153.23944 42.84813 lineto closepath pgfstr 176.11679 44.34254 moveto 176.9796 42.84813 lineto 175.254 42.84813 lineto closepath pgfstr 198.1317 44.41942 moveto 198.99449 42.925 lineto 197.26889 42.925 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 22.01154 21.05545 moveto 22.87433 19.56104 lineto 21.14873 19.56104 lineto closepath pgfstr 44.0291 25.5899 moveto 44.8919 24.09549 lineto 43.1663 24.09549 lineto closepath pgfstr 66.04367 27.89557 moveto 66.90646 26.40115 lineto 65.18086 26.40115 lineto closepath pgfstr 88.05653 29.04839 moveto 88.91934 27.55397 lineto 87.19374 27.55397 lineto closepath pgfstr 110.07077 29.66322 moveto 110.93358 28.16881 lineto 109.20796 28.16881 lineto closepath pgfstr 132.08533 29.89378 moveto 132.94814 28.39937 lineto 131.22253 28.39937 lineto closepath pgfstr 154.10225 30.0475 moveto 154.96506 28.55309 lineto 153.23944 28.55309 lineto closepath pgfstr 176.11679 30.12436 moveto 176.9796 28.62994 lineto 175.254 28.62994 lineto closepath pgfstr 198.1317 30.12436 moveto 198.99449 28.62994 lineto 197.26889 28.62994 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 22.01154 13.06252 moveto 22.87433 11.5681 lineto 21.14873 11.5681 lineto closepath pgfstr 44.0291 17.98125 moveto 44.8919 16.48683 lineto 43.1663 16.48683 lineto closepath pgfstr 66.04367 20.67117 moveto 66.90646 19.17676 lineto 65.18086 19.17676 lineto closepath pgfstr 88.05653 21.9777 moveto 88.91934 20.48329 lineto 87.19374 20.48329 lineto closepath pgfstr 110.07077 22.6694 moveto 110.93358 21.17499 lineto 109.20796 21.17499 lineto closepath pgfstr 132.08533 23.05368 moveto 132.94814 21.55927 lineto 131.22253 21.55927 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 22.01154 9.1429 moveto 22.87433 7.64848 lineto 21.14873 7.64848 lineto closepath pgfstr 44.0291 14.29219 moveto 44.8919 12.79778 lineto 43.1663 12.79778 lineto closepath pgfstr 66.04367 17.05899 moveto 66.90646 15.56458 lineto 65.18086 15.56458 lineto closepath pgfstr 88.05653 18.59608 moveto 88.91934 17.10167 lineto 87.19374 17.10167 lineto closepath pgfstr pgfstr restore save save [1.0 0.0 0.0 1.0 98.98003 -22.75941 ] concat pgfs 476 1638 a 0 setgray 476 1638 a FD(p)476 1638 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -25.21674 69.23131 ] concat pgfs 476 1638 a 0 setgray 476 1638 a FD(P)529 1650 y FG(stic)n(k)476 1638 y pgfr restore restore restore newpath restore pgfc 182 1872 a pgfr restore save restore save restore restore newpath restore pgfc 1207 1872 a 1207 1872 a 1207 1872 a pgfo save 0 setgray 0.3985 pgfw save save restore save restore save [0.49 0.0 0.0 0.49 0.0 0.0 ] concat pgfs 1207 1872 a pgfr restore save restore save restore save restore save restore save [0.49 0.0 0.0 0.49 -20.74727 -13.72856 ] concat pgfs 1523 1911 a 1523 1911 a 1523 1911 a pgfo save 0 setgray 0.3985 pgfw save save save 4.34949 -109.05504 moveto 198.62341 -109.05504 lineto 198.62341 335.81693 lineto 4.34949 335.81693 lineto clip newpath save 0.19925 pgfw 0.5 TeXcolorgray 22.01154 32.68275 moveto 22.01154 36.93471 lineto 44.02307 32.68275 moveto 44.02307 36.93471 lineto 66.0346 32.68275 moveto 66.0346 36.93471 lineto 88.04614 32.68275 moveto 88.04614 36.93471 lineto 110.05768 32.68275 moveto 110.05768 36.93471 lineto 132.06921 32.68275 moveto 132.06921 36.93471 lineto 154.08075 32.68275 moveto 154.08075 36.93471 lineto 176.09229 32.68275 moveto 176.09229 36.93471 lineto 198.10384 32.68275 moveto 198.10384 36.93471 lineto 22.01154 194.07912 moveto 22.01154 189.82716 lineto 44.02307 194.07912 moveto 44.02307 189.82716 lineto 66.0346 194.07912 moveto 66.0346 189.82716 lineto 88.04614 194.07912 moveto 88.04614 189.82716 lineto 110.05768 194.07912 moveto 110.05768 189.82716 lineto 132.06921 194.07912 moveto 132.06921 189.82716 lineto 154.08075 194.07912 moveto 154.08075 189.82716 lineto 176.09229 194.07912 moveto 176.09229 189.82716 lineto 198.10384 194.07912 moveto 198.10384 189.82716 lineto pgfstr 0 TeXcolorgray restore restore save -137.1808 32.68275 moveto -137.1808 194.07912 lineto 340.15375 194.07912 lineto 340.15375 32.68275 lineto clip newpath save 0.19925 pgfw 0.5 TeXcolorgray 4.34949 32.68275 moveto 8.59521 32.68275 lineto 4.34949 73.03185 moveto 8.59521 73.03185 lineto 4.34949 113.38094 moveto 8.59521 113.38094 lineto 4.34949 153.73003 moveto 8.59521 153.73003 lineto 4.34949 194.07912 moveto 8.59521 194.07912 lineto 198.62341 32.68275 moveto 194.37769 32.68275 lineto 198.62341 73.03185 moveto 194.37769 73.03185 lineto 198.62341 113.38094 moveto 194.37769 113.38094 lineto 198.62341 153.73003 moveto 194.37769 153.73003 lineto 198.62341 194.07912 moveto 194.37769 194.07912 lineto pgfstr 0 TeXcolorgray restore restore 4.34949 32.68275 moveto 4.34949 194.07912 lineto 198.62341 194.07912 lineto 198.62341 32.68275 lineto 4.34949 32.68275 lineto closepath pgfstr save save [1.0 0.0 0.0 1.0 17.28612 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(1)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 39.29765 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(2)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 61.30919 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(3)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 83.32072 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(4)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 105.33226 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(5)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 127.3438 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(6)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 149.35535 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(7)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 171.36688 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(8)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 193.37842 21.05322 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(2)1565 1881 y FG(9)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -16.88196 29.47253 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(0)p FD(:)p FE(28)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -16.88196 69.82162 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(0)p FD(:)p FE(29)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -11.90054 110.17072 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(0)p FD(:)p FE(3)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -16.88196 150.5198 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(0)p FD(:)p FE(31)1523 1911 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -16.88196 190.8689 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FE(0)p FD(:)p FE(32)1523 1911 y pgfr restore restore 4.34949 32.68275 moveto 198.62341 32.68275 lineto 198.62341 194.07912 lineto 4.34949 194.07912 lineto closepath clip newpath save 0 setgray 22.01154 247.74341 moveto 44.0291 154.53702 lineto 66.04367 109.74953 lineto 88.05653 87.96101 lineto 110.07077 77.06676 lineto 132.08533 71.82138 lineto 154.10225 68.99693 lineto 176.11679 67.78647 lineto 198.1317 66.97948 lineto 220.14626 66.57599 lineto 242.16081 66.57599 lineto 264.17471 66.57599 lineto 286.18925 66.57599 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 64.96204 moveto 167.28748 64.96204 lineto 170.54272 64.96204 lineto 173.79796 64.96204 lineto 177.0532 64.96204 lineto 180.30846 64.96204 lineto 183.5637 64.96204 lineto 186.81894 64.96204 lineto 190.07419 64.96204 lineto 193.32944 64.96204 lineto 196.58469 64.96204 lineto 199.83992 64.96204 lineto 203.09517 64.96204 lineto 206.35042 64.96204 lineto 209.60568 64.96204 lineto 212.86092 64.96204 lineto 216.11617 64.96204 lineto 219.37141 64.96204 lineto 222.62666 64.96204 lineto 225.8819 64.96204 lineto 229.13715 64.96204 lineto 232.3924 64.96204 lineto 235.64764 64.96204 lineto 238.90288 64.96204 lineto 242.15813 64.96204 lineto pgfstr restore save 0 setgray 22.01154 119.4333 moveto 44.0291 119.02982 lineto 66.04367 119.83679 lineto 88.05653 120.24028 lineto 110.07077 120.64377 lineto 132.08533 121.04727 lineto 154.10225 121.04727 lineto 176.11679 121.04727 lineto 198.1317 121.04727 lineto 220.14626 121.04727 lineto 242.16081 121.04727 lineto 264.17471 121.04727 lineto 286.18925 121.04727 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 117.41585 moveto 167.28748 117.41585 lineto 170.54272 117.41585 lineto 173.79796 117.41585 lineto 177.0532 117.41585 lineto 180.30846 117.41585 lineto 183.5637 117.41585 lineto 186.81894 117.41585 lineto 190.07419 117.41585 lineto 193.32944 117.41585 lineto 196.58469 117.41585 lineto 199.83992 117.41585 lineto 203.09517 117.41585 lineto 206.35042 117.41585 lineto 209.60568 117.41585 lineto 212.86092 117.41585 lineto 216.11617 117.41585 lineto 219.37141 117.41585 lineto 222.62666 117.41585 lineto 225.8819 117.41585 lineto 229.13715 117.41585 lineto 232.3924 117.41585 lineto 235.64764 117.41585 lineto 238.90288 117.41585 lineto 242.15813 117.41585 lineto pgfstr restore save 0 setgray 22.01154 51.24333 moveto 44.0291 92.39941 lineto 66.04367 115.39839 lineto 88.05653 127.09962 lineto 110.07077 133.152 lineto 132.08533 136.37991 lineto 154.10225 137.99388 lineto 176.11679 138.80087 lineto 198.1317 138.80087 lineto 220.14626 139.20436 lineto 242.16081 139.20436 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 137.5904 moveto 167.28748 137.5904 lineto 170.54272 137.5904 lineto 173.79796 137.5904 lineto 177.0532 137.5904 lineto 180.30846 137.5904 lineto 183.5637 137.5904 lineto 186.81894 137.5904 lineto 190.07419 137.5904 lineto 193.32944 137.5904 lineto 196.58469 137.5904 lineto 199.83992 137.5904 lineto 203.09517 137.5904 lineto 206.35042 137.5904 lineto 209.60568 137.5904 lineto 212.86092 137.5904 lineto 216.11617 137.5904 lineto 219.37141 137.5904 lineto 222.62666 137.5904 lineto 225.8819 137.5904 lineto 229.13715 137.5904 lineto 232.3924 137.5904 lineto 235.64764 137.5904 lineto 238.90288 137.5904 lineto 242.15813 137.5904 lineto pgfstr restore save 0 setgray 22.01154 19.77104 moveto 44.0291 79.08421 lineto 66.04367 111.76697 lineto 88.05653 128.7136 lineto 110.07077 137.5904 lineto 132.08533 142.0288 lineto 154.10225 144.44974 lineto 176.11679 145.25671 lineto 198.1317 146.0637 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 149.69511 moveto 167.28748 149.69511 lineto 170.54272 149.69511 lineto 173.79796 149.69511 lineto 177.0532 149.69511 lineto 180.30846 149.69511 lineto 183.5637 149.69511 lineto 186.81894 149.69511 lineto 190.07419 149.69511 lineto 193.32944 149.69511 lineto 196.58469 149.69511 lineto 199.83992 149.69511 lineto 203.09517 149.69511 lineto 206.35042 149.69511 lineto 209.60568 149.69511 lineto 212.86092 149.69511 lineto 216.11617 149.69511 lineto 219.37141 149.69511 lineto 222.62666 149.69511 lineto 225.8819 149.69511 lineto 229.13715 149.69511 lineto 232.3924 149.69511 lineto 235.64764 149.69511 lineto 238.90288 149.69511 lineto 242.15813 149.69511 lineto pgfstr restore save 0 setgray 22.01154 5.64886 moveto 44.0291 73.03185 lineto 66.04367 110.15302 lineto 88.05653 129.52057 lineto 110.07077 139.60785 lineto 132.08533 144.85323 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 148.88814 moveto 167.28748 148.88814 lineto 170.54272 148.88814 lineto 173.79796 148.88814 lineto 177.0532 148.88814 lineto 180.30846 148.88814 lineto 183.5637 148.88814 lineto 186.81894 148.88814 lineto 190.07419 148.88814 lineto 193.32944 148.88814 lineto 196.58469 148.88814 lineto 199.83992 148.88814 lineto 203.09517 148.88814 lineto 206.35042 148.88814 lineto 209.60568 148.88814 lineto 212.86092 148.88814 lineto 216.11617 148.88814 lineto 219.37141 148.88814 lineto 222.62666 148.88814 lineto 225.8819 148.88814 lineto 229.13715 148.88814 lineto 232.3924 148.88814 lineto 235.64764 148.88814 lineto 238.90288 148.88814 lineto 242.15813 148.88814 lineto pgfstr restore save 0 setgray 22.01154 0.0 moveto 44.0291 70.6109 lineto 66.04367 109.34602 lineto 88.05653 129.92407 lineto pgfstr restore restore save 0 setgray 0 setgray 44.0291 155.5333 moveto 44.8919 154.03888 lineto 43.1663 154.03888 lineto closepath pgfstr 66.04367 110.7458 moveto 66.90646 109.25139 lineto 65.18086 109.25139 lineto closepath pgfstr 88.05653 88.95729 moveto 88.91934 87.46288 lineto 87.19374 87.46288 lineto closepath pgfstr 110.07077 78.06303 moveto 110.93358 76.56862 lineto 109.20796 76.56862 lineto closepath pgfstr 132.08533 72.81766 moveto 132.94814 71.32324 lineto 131.22253 71.32324 lineto closepath pgfstr 154.10225 69.99321 moveto 154.96506 68.4988 lineto 153.23944 68.4988 lineto closepath pgfstr 176.11679 68.78275 moveto 176.9796 67.28833 lineto 175.254 67.28833 lineto closepath pgfstr 198.1317 67.97575 moveto 198.99449 66.48134 lineto 197.26889 66.48134 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 22.01154 120.42958 moveto 22.87433 118.93517 lineto 21.14873 118.93517 lineto closepath pgfstr 44.0291 120.0261 moveto 44.8919 118.53168 lineto 43.1663 118.53168 lineto closepath pgfstr 66.04367 120.83307 moveto 66.90646 119.33865 lineto 65.18086 119.33865 lineto closepath pgfstr 88.05653 121.23656 moveto 88.91934 119.74214 lineto 87.19374 119.74214 lineto closepath pgfstr 110.07077 121.64005 moveto 110.93358 120.14563 lineto 109.20796 120.14563 lineto closepath pgfstr 132.08533 122.04355 moveto 132.94814 120.54913 lineto 131.22253 120.54913 lineto closepath pgfstr 154.10225 122.04355 moveto 154.96506 120.54913 lineto 153.23944 120.54913 lineto closepath pgfstr 176.11679 122.04355 moveto 176.9796 120.54913 lineto 175.254 120.54913 lineto closepath pgfstr 198.1317 122.04355 moveto 198.99449 120.54913 lineto 197.26889 120.54913 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 22.01154 52.23961 moveto 22.87433 50.7452 lineto 21.14873 50.7452 lineto closepath pgfstr 44.0291 93.39569 moveto 44.8919 91.90128 lineto 43.1663 91.90128 lineto closepath pgfstr 66.04367 116.39467 moveto 66.90646 114.90025 lineto 65.18086 114.90025 lineto closepath pgfstr 88.05653 128.0959 moveto 88.91934 126.60149 lineto 87.19374 126.60149 lineto closepath pgfstr 110.07077 134.14827 moveto 110.93358 132.65385 lineto 109.20796 132.65385 lineto closepath pgfstr 132.08533 137.37619 moveto 132.94814 135.88177 lineto 131.22253 135.88177 lineto closepath pgfstr 154.10225 138.99016 moveto 154.96506 137.49574 lineto 153.23944 137.49574 lineto closepath pgfstr 176.11679 139.79715 moveto 176.9796 138.30273 lineto 175.254 138.30273 lineto closepath pgfstr 198.1317 139.79715 moveto 198.99449 138.30273 lineto 197.26889 138.30273 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 44.0291 80.08049 moveto 44.8919 78.58607 lineto 43.1663 78.58607 lineto closepath pgfstr 66.04367 112.76324 moveto 66.90646 111.26883 lineto 65.18086 111.26883 lineto closepath pgfstr 88.05653 129.70987 moveto 88.91934 128.21545 lineto 87.19374 128.21545 lineto closepath pgfstr 110.07077 138.58667 moveto 110.93358 137.09225 lineto 109.20796 137.09225 lineto closepath pgfstr 132.08533 143.02507 moveto 132.94814 141.53065 lineto 131.22253 141.53065 lineto closepath pgfstr 154.10225 145.44601 moveto 154.96506 143.9516 lineto 153.23944 143.9516 lineto closepath pgfstr 176.11679 146.25299 moveto 176.9796 144.75858 lineto 175.254 144.75858 lineto closepath pgfstr 198.1317 147.05998 moveto 198.99449 145.56557 lineto 197.26889 145.56557 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 44.0291 74.02812 moveto 44.8919 72.5337 lineto 43.1663 72.5337 lineto closepath pgfstr 66.04367 111.14929 moveto 66.90646 109.65488 lineto 65.18086 109.65488 lineto closepath pgfstr 88.05653 130.51685 moveto 88.91934 129.02243 lineto 87.19374 129.02243 lineto closepath pgfstr 110.07077 140.60413 moveto 110.93358 139.10971 lineto 109.20796 139.10971 lineto closepath pgfstr 132.08533 145.8495 moveto 132.94814 144.35509 lineto 131.22253 144.35509 lineto closepath pgfstr pgfstr restore save 0 setgray 0 setgray 44.0291 71.60718 moveto 44.8919 70.11276 lineto 43.1663 70.11276 lineto closepath pgfstr 66.04367 110.3423 moveto 66.90646 108.84789 lineto 65.18086 108.84789 lineto closepath pgfstr 88.05653 130.92035 moveto 88.91934 129.42593 lineto 87.19374 129.42593 lineto closepath pgfstr pgfstr restore save save [1.0 0.0 0.0 1.0 98.98003 9.92332 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FD(p)1523 1911 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -26.21243 98.19562 ] concat pgfs 1523 1911 a 0 setgray 1523 1911 a FA(E)8 b FB(r)p 0 TeXcolorgray FD(V)1674 1881 y Fy(\016)p 0 TeXcolorgray 6 w FG(2)1748 1911 y FB(s)1523 1911 y pgfr restore restore restore newpath restore pgfc 1207 1872 a pgfr restore save restore save restore restore newpath restore pgfc 2231 1872 a 2231 1872 a 2231 1872 a pgfo save 0 setgray 0.3985 pgfw save save restore save restore save [0.49 0.0 0.0 0.49 0.0 0.0 ] concat pgfs 2231 1872 a pgfr restore save restore save restore save restore save restore save [0.49 0.0 0.0 0.49 -20.74727 -13.72856 ] concat pgfs 2548 1638 a 2548 1638 a 2548 1638 a pgfo save 0 setgray 0.3985 pgfw save save save 4.34949 -141.73969 moveto 198.62341 -141.73969 lineto 198.62341 303.13544 lineto 4.34949 303.13544 lineto clip newpath save 0.19925 pgfw 0.5 TeXcolorgray 22.01154 0.0 moveto 22.01154 4.25198 lineto 44.02307 0.0 moveto 44.02307 4.25198 lineto 66.0346 0.0 moveto 66.0346 4.25198 lineto 88.04614 0.0 moveto 88.04614 4.25198 lineto 110.05768 0.0 moveto 110.05768 4.25198 lineto 132.06921 0.0 moveto 132.06921 4.25198 lineto 154.08075 0.0 moveto 154.08075 4.25198 lineto 176.09229 0.0 moveto 176.09229 4.25198 lineto 198.10384 0.0 moveto 198.10384 4.25198 lineto 22.01154 161.39575 moveto 22.01154 157.14374 lineto 44.02307 161.39575 moveto 44.02307 157.14374 lineto 66.0346 161.39575 moveto 66.0346 157.14374 lineto 88.04614 161.39575 moveto 88.04614 157.14374 lineto 110.05768 161.39575 moveto 110.05768 157.14374 lineto 132.06921 161.39575 moveto 132.06921 157.14374 lineto 154.08075 161.39575 moveto 154.08075 157.14374 lineto 176.09229 161.39575 moveto 176.09229 157.14374 lineto 198.10384 161.39575 moveto 198.10384 157.14374 lineto pgfstr 0 TeXcolorgray restore restore save -137.1808 0.0 moveto -137.1808 161.39575 lineto 340.15375 161.39575 lineto 340.15375 0.0 lineto clip newpath save 0.19925 pgfw 0.5 TeXcolorgray 4.34949 7.6855 moveto 8.59521 7.6855 lineto 4.34949 46.11307 moveto 8.59521 46.11307 lineto 4.34949 84.54062 moveto 8.59521 84.54062 lineto 4.34949 122.96819 moveto 8.59521 122.96819 lineto 4.34949 161.39575 moveto 8.59521 161.39575 lineto 198.62341 7.6855 moveto 194.37769 7.6855 lineto 198.62341 46.11307 moveto 194.37769 46.11307 lineto 198.62341 84.54062 moveto 194.37769 84.54062 lineto 198.62341 122.96819 moveto 194.37769 122.96819 lineto 198.62341 161.39575 moveto 194.37769 161.39575 lineto pgfstr 0 TeXcolorgray restore restore 4.34949 0.0 moveto 4.34949 161.39575 lineto 198.62341 161.39575 lineto 198.62341 0.0 lineto 4.34949 0.0 lineto closepath pgfstr save save [1.0 0.0 0.0 1.0 17.28612 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(1)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 39.29765 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(2)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 61.30919 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(3)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 83.32072 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(4)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 105.33226 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(5)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 127.3438 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(6)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 149.35535 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(7)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 171.36688 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(8)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 193.37842 -11.62952 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(2)2590 1608 y FG(9)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -11.90054 4.47528 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(0)p FD(:)p FE(6)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -16.88196 42.90285 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(0)p FD(:)p FE(65)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -11.90054 81.33041 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(0)p FD(:)p FE(7)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -16.88196 119.75797 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(0)p FD(:)p FE(75)2548 1638 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -11.90054 158.18553 ] concat pgfs 2548 1638 a 0 setgray 2548 1638 a FE(0)p FD(:)p FE(8)2548 1638 y pgfr restore restore 4.34949 0.0 moveto 198.62341 0.0 lineto 198.62341 161.39575 lineto 4.34949 161.39575 lineto closepath clip newpath save 0 setgray 22.01154 85.6166 moveto 44.0291 118.35687 lineto 66.04367 135.72614 lineto 88.05653 144.64133 lineto 110.07077 149.09892 lineto 132.08533 151.32773 lineto 154.10225 152.48055 lineto 176.11679 153.0954 lineto 198.1317 153.32596 lineto 220.14626 153.47968 lineto 242.16081 153.55652 lineto 264.17471 153.55652 lineto 286.18925 153.55652 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 152.94168 moveto 165.42139 152.94168 lineto 166.81053 152.94168 lineto 168.19968 152.94168 lineto 169.58884 152.94168 lineto 170.978 152.94168 lineto 172.36716 152.94168 lineto 173.75632 152.94168 lineto 175.14546 152.94168 lineto 176.53462 152.94168 lineto 177.92378 152.94168 lineto 179.31294 152.94168 lineto 180.70209 152.94168 lineto 182.09125 152.94168 lineto 183.48041 152.94168 lineto 184.86957 152.94168 lineto 186.25873 152.94168 lineto 187.64787 152.94168 lineto 189.03702 152.94168 lineto 190.42618 152.94168 lineto 191.81534 152.94168 lineto 193.20448 152.94168 lineto 194.59364 152.94168 lineto 195.9828 152.94168 lineto 197.37196 152.94168 lineto pgfstr restore save 0 setgray 22.01154 41.50175 moveto 44.0291 76.47084 lineto 66.04367 95.30034 lineto 88.05653 104.98409 lineto 110.07077 109.97966 lineto 132.08533 112.43903 lineto 154.10225 113.66872 lineto 176.11679 114.3604 lineto 198.1317 114.66783 lineto 220.14626 114.82153 lineto 242.16081 114.8984 lineto 264.17471 114.8984 lineto 286.18925 114.8984 lineto pgfstr restore save 1 0 0 setrgbcolor 0.79701 pgfw [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 164.03223 114.51413 moveto 165.42139 114.51413 lineto 166.81053 114.51413 lineto 168.19968 114.51413 lineto 169.58884 114.51413 lineto 170.978 114.51413 lineto 172.36716 114.51413 lineto 173.75632 114.51413 lineto 175.14546 114.51413 lineto 176.53462 114.51413 lineto 177.92378 114.51413 lineto 179.31294 114.51413 lineto 180.70209 114.51413 lineto 182.09125 114.51413 lineto 183.48041 114.51413 lineto 184.86957 114.51413 lineto 186.25873 114.51413 lineto 187.64787 114.51413 lineto 189.03702 114.51413 lineto 190.42618 114.51413 lineto 191.81534 114.51413 lineto 193.20448 114.51413 lineto 194.59364 114.51413 lineto 195.9828 114.51413 lineto 197.37196 114.51413 lineto pgfstr restore save 0 setgray 22.01154 20.82773 moveto 44.0291 55.18196 lineto 66.04367 73.93462 lineto 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-69.59753 4.08429 moveto gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath -50.45644 4.05045 moveto -50.45644 4.6007 -50.90248 5.04672 -51.45271 5.04672 curveto -52.00294 5.04672 -52.44899 4.6007 -52.44899 4.05045 curveto -52.44899 3.50021 -52.00294 3.05417 -51.45271 3.05417 curveto -50.90248 3.05417 -50.45644 3.50021 -50.45644 4.05045 curveto closepath -51.45271 4.05045 moveto gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath -32.31053 3.80225 moveto -32.31053 4.3525 -32.75658 4.79852 -33.30681 4.79852 curveto -33.85706 4.79852 -34.30309 4.3525 -34.30309 3.80225 curveto -34.30309 3.25201 -33.85706 2.80597 -33.30681 2.80597 curveto -32.75658 2.80597 -32.31053 3.25201 -32.31053 3.80225 curveto closepath -33.30681 3.80225 moveto gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath -14.16571 2.02448 moveto -14.16571 2.5747 -14.61176 3.02075 -15.16199 3.02075 curveto -15.71222 3.02075 -16.15826 2.5747 -16.15826 2.02448 curveto -16.15826 1.47423 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-89.23012 39.27298 -89.23012 curveto 38.72275 -89.23012 38.2767 -89.67616 38.2767 -90.2264 curveto 38.2767 -90.77663 38.72275 -91.22267 39.27298 -91.22267 curveto 39.82321 -91.22267 40.26926 -90.77663 40.26926 -90.2264 curveto closepath 39.27298 -90.2264 moveto gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath pgfstr restore save save [1.0 0.0 0.0 1.0 -30.17455 -177.49469 ] concat pgfs 1630 -641 a 0 setgray 1630 -641 a FD(!)1630 -641 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -157.42903 -87.70355 ] concat pgfs 1630 -641 a 0 setgray 1630 -641 a FD(S)1681 -629 y Fy(V)1739 -641 y FB(p)p FD(!)s FB(q)1630 -641 y pgfr restore restore save /pgffc{1 setgray}def /pgfsc{0 setgray}def save /pgffc{1 setgray}def /pgfsc{0 setgray}def 43.06334 62.09804 -123.83273 -154.53601 pgfe gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath restore save [1.0 0.0 0.0 1.0 -120.8439 -145.74887 ] concat pgfs 1633 -861 a 1633 -861 a 1633 -861 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 0.79701 0.99628 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 1938 -861 a 1938 -861 a 1938 -861 a pgfo save save save [1.0 0.0 0.0 1.0 -11.87302 -2.46303 ] concat pgfs 1938 -861 a /pgfsc{}def/pgffc{}def 1938 -861 a 1938 -861 a 0 setgray 1938 -861 a FD(\034)33 b FB(\020)23 b FE(1)1938 -861 y pgfr restore restore restore pgfc 1633 -755 a 1633 -755 a 1633 -755 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 1938 -755 a 1938 -755 a 1938 -755 a pgfo save save save [1.0 0.0 0.0 1.0 -17.16501 -3.30766 ] concat pgfs 1938 -755 a /pgfsc{}def/pgffc{}def 1938 -755 a 1938 -755 a 0 setgray 1938 -755 a FD(\034)33 b FB(\020)23 b FE(2)2137 -785 y Fx(\001)p FG(1)1938 -755 y pgfr restore restore restore pgfc 1633 -641 a 1633 -641 a 1633 -641 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 1938 -641 a 1938 -641 a 1938 -641 a pgfo save save save [1.0 0.0 0.0 1.0 -17.16501 -3.30766 ] concat pgfs 1938 -641 a /pgfsc{}def/pgffc{}def 1938 -641 a 1938 -641 a 0 setgray 1938 -641 a FD(\034)33 b FB(\020)23 b FE(2)2137 -672 y Fx(\001)p FG(2)1938 -641 y pgfr restore restore restore pgfc 1630 -641 a pgfr restore restore restore newpath restore pgfc 228 865 a pgfr restore save restore save restore restore newpath restore pgfc 1231 865 a 1231 865 a 1231 865 a pgfo save 0 setgray 0.3985 pgfw save save restore save restore save [0.49 0.0 0.0 0.49 0.0 0.0 ] concat pgfs 1231 865 a pgfr restore save restore save restore save restore save restore save [0.49 0.0 0.0 0.49 -21.65228 -12.77933 ] concat pgfs 2632 -642 a 2632 -642 a 2632 -642 a pgfo save 0 setgray 0.3985 pgfw save save save -124.032 -296.38736 moveto 70.24193 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Fx(\001)p FG(3)2632 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -92.96136 -166.38847 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FE(10)2716 -672 y Fx(\001)p FG(2)2632 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -51.61737 -166.38847 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FE(10)2716 -672 y Fx(\001)p FG(1)2632 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -7.2161 -166.38847 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FE(10)2716 -672 y FG(0)2632 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 34.12788 -166.38847 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FE(10)2716 -672 y FG(1)2632 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -148.09856 -154.8484 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FE(10)2716 -672 y Fx(\001)p FG(4)2632 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -148.09856 -117.15001 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FE(10)2716 -672 y Fx(\001)p FG(3)2632 -642 y pgfr restore restore 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curveto 20.13051 -40.22319 20.57655 -40.66924 21.12679 -40.66924 curveto 21.67703 -40.66924 22.12306 -40.22319 22.12306 -39.67296 curveto closepath 21.12679 -39.67296 moveto gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath 40.26926 -90.4482 moveto 40.26926 -89.89795 39.82321 -89.45192 39.27298 -89.45192 curveto 38.72275 -89.45192 38.2767 -89.89795 38.2767 -90.4482 curveto 38.2767 -90.99843 38.72275 -91.44447 39.27298 -91.44447 curveto 39.82321 -91.44447 40.26926 -90.99843 40.26926 -90.4482 curveto closepath 39.27298 -90.4482 moveto gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath pgfstr restore save save [1.0 0.0 0.0 1.0 -30.17455 -177.51837 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FD(!)2632 -642 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -157.42903 -87.7272 ] concat pgfs 2632 -642 a 0 setgray 2632 -642 a FD(S)2683 -630 y Fy(V)2741 -642 y FB(p)p FD(!)s FB(q)2632 -642 y pgfr restore restore save /pgffc{1 setgray}def /pgfsc{0 setgray}def save /pgffc{1 setgray}def /pgfsc{0 setgray}def 43.06334 62.09804 -123.83273 -154.5597 pgfe gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath restore save [1.0 0.0 0.0 1.0 -120.8439 -145.77255 ] concat pgfs 2635 -861 a 2635 -861 a 2635 -861 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 0.79701 0.99628 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 2941 -861 a 2941 -861 a 2941 -861 a pgfo save save save [1.0 0.0 0.0 1.0 -11.87302 -2.46303 ] concat pgfs 2941 -861 a /pgfsc{}def/pgffc{}def 2941 -861 a 2941 -861 a 0 setgray 2941 -861 a FD(\034)32 b FB(\020)23 b FE(1)2941 -861 y pgfr restore restore restore pgfc 2635 -755 a 2635 -755 a 2635 -755 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 2941 -755 a 2941 -755 a 2941 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TeXcolorgray restore restore -124.032 -154.81776 moveto -124.032 6.57909 lineto 70.24193 6.57909 lineto 70.24193 -154.81776 lineto -124.032 -154.81776 lineto closepath pgfstr save save [1.0 0.0 0.0 1.0 -134.30537 -166.4473 ] concat pgfs 3635 -642 a 0 setgray 3635 -642 a FE(10)3719 -672 y Fx(\001)p FG(3)3635 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -92.96136 -166.4473 ] concat pgfs 3635 -642 a 0 setgray 3635 -642 a FE(10)3719 -672 y Fx(\001)p FG(2)3635 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -51.61737 -166.4473 ] concat pgfs 3635 -642 a 0 setgray 3635 -642 a FE(10)3719 -672 y Fx(\001)p FG(1)3635 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -7.2161 -166.4473 ] concat pgfs 3635 -642 a 0 setgray 3635 -642 a FE(10)3719 -672 y FG(0)3635 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 34.12788 -166.4473 ] concat pgfs 3635 -642 a 0 setgray 3635 -642 a FE(10)3719 -672 y FG(1)3635 -642 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -148.09856 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38.2767 -91.81741 38.2767 -92.36766 curveto 38.2767 -92.9179 38.72275 -93.36394 39.27298 -93.36394 curveto 39.82321 -93.36394 40.26926 -92.9179 40.26926 -92.36766 curveto closepath 39.27298 -92.36766 moveto gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath pgfstr restore save save [1.0 0.0 0.0 1.0 -30.17455 -177.5772 ] concat pgfs 3635 -642 a 0 setgray 3635 -642 a FD(!)3635 -642 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -157.42903 -87.78618 ] concat pgfs 3635 -642 a 0 setgray 3635 -642 a FD(S)3686 -630 y Fy(V)3743 -642 y FB(p)p FD(!)s FB(q)3635 -642 y pgfr restore restore save /pgffc{1 setgray}def /pgfsc{0 setgray}def save /pgffc{1 setgray}def /pgfsc{0 setgray}def 43.06334 62.09804 -123.83273 -154.61852 pgfe gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath restore save [1.0 0.0 0.0 1.0 -120.8439 -145.83138 ] concat pgfs 3638 -862 a 3638 -862 a 3638 -862 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 0.79701 0.99628 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 3943 -862 a 3943 -862 a 3943 -862 a pgfo save save save [1.0 0.0 0.0 1.0 -11.87302 -2.46303 ] concat pgfs 3943 -862 a /pgfsc{}def/pgffc{}def 3943 -862 a 3943 -862 a 0 setgray 3943 -862 a FD(\034)32 b FB(\020)23 b FE(1)3943 -862 y pgfr restore restore restore pgfc 3638 -755 a 3638 -755 a 3638 -755 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 3943 -755 a 3943 -755 a 3943 -755 a pgfo save save save [1.0 0.0 0.0 1.0 -17.16501 -3.30766 ] concat pgfs 3943 -755 a /pgfsc{}def/pgffc{}def 3943 -755 a 3943 -755 a 0 setgray 3943 -755 a FD(\034)32 b FB(\020)23 b FE(2)4141 -786 y Fx(\001)p FG(1)3943 -755 y pgfr restore restore restore pgfc 3638 -642 a 3638 -642 a 3638 -642 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 3943 -642 a 3943 -642 a 3943 -642 a pgfo save save save [1.0 0.0 0.0 1.0 -17.16501 -3.30766 ] concat pgfs 3943 -642 a /pgfsc{}def/pgffc{}def 3943 -642 a 3943 -642 a 0 setgray 3943 -642 a FD(\034)32 b FB(\020)23 b FE(2)4141 -672 y Fx(\001)p FG(2)3943 -642 y pgfr restore restore restore pgfc 3635 -642 a pgfr restore restore restore newpath restore pgfc 2233 865 a pgfr restore save restore save restore restore newpath restore pgfc 228 1642 a 228 1642 a 228 1642 a pgfo save 0 setgray 0.3985 pgfw save save restore save restore save [0.49 0.0 0.0 0.49 0.0 0.0 ] concat pgfs 228 1642 a pgfr restore save restore save restore save restore save restore save [0.49 0.0 0.0 0.49 -21.65228 -12.77933 ] concat pgfs 1630 135 a 1630 135 a 1630 135 a pgfo save 0 setgray 0.3985 pgfw save save save -124.032 -296.31244 moveto 70.24193 -296.31244 lineto 70.24193 148.18417 lineto -124.032 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pgfsc pgfstr grestore newpath pgfstr restore save save [1.0 0.0 0.0 1.0 -30.17455 -177.52197 ] concat pgfs 1630 135 a 0 setgray 1630 135 a FD(!)1630 135 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -157.42903 -87.73085 ] concat pgfs 1630 135 a 0 setgray 1630 135 a FD(S)1681 147 y Fy(V)1739 135 y FB(p)p FD(!)s FB(q)1630 135 y pgfr restore restore save /pgffc{1 setgray}def /pgfsc{0 setgray}def save /pgffc{1 setgray}def /pgfsc{0 setgray}def 43.06334 62.09804 -123.83273 -154.5633 pgfe gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath restore save [1.0 0.0 0.0 1.0 -120.8439 -145.77615 ] concat pgfs 1633 -84 a 1633 -84 a 1633 -84 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 0.79701 0.99628 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 1938 -84 a 1938 -84 a 1938 -84 a pgfo save save save [1.0 0.0 0.0 1.0 -11.87302 -2.46303 ] concat pgfs 1938 -84 a /pgfsc{}def/pgffc{}def 1938 -84 a 1938 -84 a 0 setgray 1938 -84 a FD(\034)33 b FB(\020)23 b FE(1)1938 -84 y pgfr restore restore restore pgfc 1633 22 a 1633 22 a 1633 22 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 1938 22 a 1938 22 a 1938 22 a pgfo save save save [1.0 0.0 0.0 1.0 -17.16501 -3.30766 ] concat pgfs 1938 22 a /pgfsc{}def/pgffc{}def 1938 22 a 1938 22 a 0 setgray 1938 22 a FD(\034)33 b FB(\020)23 b FE(2)2137 -8 y Fx(\001)p FG(1)1938 22 y pgfr restore restore restore pgfc 1633 135 a 1633 135 a 1633 135 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 1938 135 a 1938 135 a 1938 135 a pgfo save save save [1.0 0.0 0.0 1.0 -17.16501 -3.30766 ] concat pgfs 1938 135 a /pgfsc{}def/pgffc{}def 1938 135 a 1938 135 a 0 setgray 1938 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restore save save [0.0 1.0 -1.0 0.0 -157.42903 -87.79073 ] concat pgfs 3635 135 a 0 setgray 3635 135 a FD(S)3686 147 y Fy(V)3743 135 y FB(p)p FD(!)s FB(q)3635 135 y pgfr restore restore save /pgffc{1 setgray}def /pgfsc{0 setgray}def save /pgffc{1 setgray}def /pgfsc{0 setgray}def 43.06334 62.09804 -123.83273 -154.6232 pgfe gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath restore save [1.0 0.0 0.0 1.0 -120.8439 -145.83607 ] concat pgfs 3638 -85 a 3638 -85 a 3638 -85 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 0.79701 0.99628 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 3943 -85 a 3943 -85 a 3943 -85 a pgfo save save save [1.0 0.0 0.0 1.0 -11.87302 -2.46303 ] concat pgfs 3943 -85 a /pgfsc{}def/pgffc{}def 3943 -85 a 3943 -85 a 0 setgray 3943 -85 a FD(\034)32 b FB(\020)23 b FE(1)3943 -85 y pgfr restore restore restore pgfc 3638 22 a 3638 22 a 3638 22 a pgfo save /pgffc{0 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save /pgffc{1 setgray}def /pgfsc{0 setgray}def save /pgffc{1 setgray}def /pgfsc{0 setgray}def 43.06334 62.09804 -123.83273 -154.55821 pgfe gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath restore save [1.0 0.0 0.0 1.0 -120.8439 -145.77107 ] concat pgfs 1633 693 a 1633 693 a 1633 693 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 0.79701 0.99628 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore pgfc 1938 693 a 1938 693 a 1938 693 a pgfo save save save [1.0 0.0 0.0 1.0 -11.87302 -2.46303 ] concat pgfs 1938 693 a /pgfsc{}def/pgffc{}def 1938 693 a 1938 693 a 0 setgray 1938 693 a FD(\034)33 b FB(\020)23 b FE(1)1938 693 y pgfr restore restore restore pgfc 1633 799 a 1633 799 a 1633 799 a pgfo save /pgffc{0 setgray}def save 0.79701 pgfw /pgfsc{}def/pgffc{}def 0.5 setgray [ 2.98883 1.99255 0.79701 1.99255 ] 0.0 setdash 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr restore restore 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save save [1.0 0.0 0.0 1.0 -7.2161 -166.44765 ] concat pgfs 3635 912 a 0 setgray 3635 912 a FE(10)3719 882 y FG(0)3635 912 y pgfr restore restore save save [1.0 0.0 0.0 1.0 34.12788 -166.44765 ] concat pgfs 3635 912 a 0 setgray 3635 912 a FE(10)3719 882 y FG(1)3635 912 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -148.09856 -153.50034 ] concat pgfs 3635 912 a 0 setgray 3635 912 a FE(10)3719 882 y Fx(\001)p FG(4)3635 912 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -148.09856 -116.13896 ] concat pgfs 3635 912 a 0 setgray 3635 912 a FE(10)3719 882 y Fx(\001)p FG(3)3635 912 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -148.09856 -78.77759 ] concat pgfs 3635 912 a 0 setgray 3635 912 a FE(10)3719 882 y Fx(\001)p FG(2)3635 912 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -148.09856 -41.41621 ] concat pgfs 3635 912 a 0 setgray 3635 912 a FE(10)3719 882 y Fx(\001)p FG(1)3635 912 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -141.98402 -4.05484 ] concat pgfs 3635 912 a 0 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31.03096 lineto 67.6302 -130.36577 lineto -126.64362 -130.36577 lineto closepath pgfstr save save [1.0 0.0 0.0 1.0 -136.91699 -141.9953 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y Fx(\001)p FG(3)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -94.70245 -141.9953 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y Fx(\001)p FG(2)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -52.48792 -141.9953 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y Fx(\001)p FG(1)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -7.2161 -141.9953 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y FG(0)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 34.99843 -141.9953 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y FG(1)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -150.71019 -128.17873 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y Fx(\001)p FG(4)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -150.71019 -97.14775 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y Fx(\001)p FG(3)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -150.71019 -66.11679 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y Fx(\001)p FG(2)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -150.71019 -35.08582 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y Fx(\001)p FG(1)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -144.59564 -4.05484 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y FG(0)3187 -187 y pgfr restore restore save save [1.0 0.0 0.0 1.0 -144.59564 26.9761 ] concat pgfs 3187 -187 a 0 setgray 3187 -187 a FE(10)3271 -217 y FG(1)3187 -187 y pgfr restore restore -126.64362 -130.36577 moveto 67.6302 -130.36577 lineto 67.6302 31.03096 lineto -126.64362 31.03096 lineto closepath clip newpath save 0.79701 pgfw 0.5 setgray [ 0.79701 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128.60612 ] concat pgfs 425 2194 a 425 2194 a 425 2194 a pgfo save /pgffc{0 setgray}def save /pgfsc{}def/pgffc{}def 0 TeXcolorgray 0.79701 pgfw 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr 0 TeXcolorgray restore restore pgfc 757 2194 a 757 2194 a 757 2194 a pgfo save save save [1.0 0.0 0.0 1.0 -20.3822 -2.57968 ] concat pgfs 757 2194 a /pgfsc{}def/pgffc{}def 757 2194 a 757 2194 a 0 setgray 757 2194 a FE(excursion)757 2194 y pgfr restore restore restore pgfc 425 2297 a 425 2297 a 425 2297 a pgfo save /pgffc{0 setgray}def save /pgfsc{}def/pgffc{}def 1 0 0 TeXcolorrgb 0.79701 pgfw 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr 0 TeXcolorgray restore restore pgfc 757 2297 a 757 2297 a 757 2297 a pgfo save save save [1.0 0.0 0.0 1.0 -18.40349 -2.7121 ] concat pgfs 757 2297 a /pgfsc{}def/pgffc{}def 757 2297 a 757 2297 a 0 setgray 757 2297 a FE(dynamic)757 2297 y pgfr restore restore restore pgfc 425 2399 a 425 2399 a 425 2399 a pgfo save /pgffc{0 setgray}def 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191.5418 27.25414 lineto 191.69353 27.699 lineto 191.84525 27.37317 lineto 191.99696 27.08153 lineto 192.1489 26.81912 lineto 192.30064 27.56761 lineto 192.45236 27.28336 lineto 192.60406 27.16905 lineto 192.756 27.208 lineto 192.90775 27.36102 lineto 193.05946 27.17154 lineto 193.21118 27.11324 lineto 193.3631 27.14001 lineto 193.51483 27.3295 lineto 193.66656 27.75728 lineto 193.81828 27.40964 lineto 193.9702 26.97462 lineto 194.12195 27.03786 lineto 194.27368 27.54825 lineto pgfstr 0 TeXcolorgray restore restore save save [1.0 0.0 0.0 1.0 87.45079 -25.12363 ] concat pgfs 1126 2399 a 0 setgray 1126 2399 a FE(time)1126 2399 y pgfr restore restore save save [0.0 1.0 -1.0 0.0 -17.83228 23.21614 ] concat pgfs 1126 2399 a 0 setgray 1126 2399 a FE(histogram)24 b(/)j(n)n(umerical)d(p)r(df) 1126 2399 y pgfr restore restore save /pgffc{1 setgray}def /pgfsc{0 setgray}def save /pgffc{1 setgray}def /pgfsc{0 setgray}def 40.6495 68.53242 125.54199 120.54303 pgfe gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath restore save [1.0 0.0 0.0 1.0 128.53082 128.60217 ] concat pgfs 1129 2194 a 1129 2194 a 1129 2194 a pgfo save /pgffc{0 setgray}def save /pgfsc{}def/pgffc{}def 0 TeXcolorgray 0.79701 pgfw 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr 0 TeXcolorgray restore restore pgfc 1460 2194 a 1460 2194 a 1460 2194 a pgfo save save save [1.0 0.0 0.0 1.0 -20.3822 -2.57968 ] concat pgfs 1460 2194 a /pgfsc{}def/pgffc{}def 1460 2194 a 1460 2194 a 0 setgray 1460 2194 a FE(excursion)1460 2194 y pgfr restore restore restore pgfc 1129 2297 a 1129 2297 a 1129 2297 a pgfo save /pgffc{0 setgray}def save /pgfsc{}def/pgffc{}def 1 0 0 TeXcolorrgb 0.79701 pgfw 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr 0 TeXcolorgray restore restore pgfc 1460 2297 a 1460 2297 a 1460 2297 a pgfo save save save [1.0 0.0 0.0 1.0 -18.40349 -2.7121 ] concat pgfs 1460 2297 a /pgfsc{}def/pgffc{}def 1460 2297 a 1460 2297 a 0 setgray 1460 2297 a FE(dynamic)1460 2297 y pgfr restore restore restore pgfc 1129 2399 a 1129 2399 a 1129 2399 a pgfo save /pgffc{0 setgray}def save /pgfsc{}def/pgffc{}def 0 0 1 TeXcolorrgb 0.79701 pgfw 0.0 0.0 moveto 8.50412 0.0 lineto 17.00826 0.0 lineto pgfstr 0 TeXcolorgray restore restore pgfc 1460 2399 a 1460 2399 a 1460 2399 a pgfo save save save [1.0 0.0 0.0 1.0 -11.92766 -2.57968 ] concat pgfs 1460 2399 a /pgfsc{}def/pgffc{}def 1460 2399 a 1460 2399 a 0 setgray 1460 2399 a FE(static)1460 2399 y pgfr restore restore restore pgfc 1126 2399 a pgfr restore restore restore newpath restore pgfc 887 2636 a pgfr restore save restore save restore save save [1.0 0.0 0.0 1.0 18.25197 29.22292 ] concat pgfs 887 2636 a 0 setgray 887 2636 a 0 TeXcolorgray FD(\026)937 2648 y FG(d)1001 2636 y FB(\020)f FE(0)p FD(:)p FE(5)p 0 TeXcolorgray 887 2636 a pgfr restore restore restore newpath restore pgfc 1632 2636 a 1632 2636 a 1632 2636 a pgfo save 0 setgray 0.3985 pgfw save save restore save restore save [0.37 0.0 0.0 0.37 0.0 0.0 ] concat pgfs 1632 2636 a pgfr restore save restore save restore save restore save restore save [0.37 0.0 0.0 0.37 -10.59108 -10.5242 ] concat pgfs 1870 2399 a 1870 2399 a 1870 2399 a pgfo save 0 setgray 0.3985 pgfw save save save 0.0 -141.74405 moveto 194.27368 -141.74405 lineto 194.27368 303.13889 lineto 0.0 303.13889 lineto clip newpath save 0.19925 pgfw 0.5 TeXcolorgray 0.0 0.0 moveto 0.0 4.25212 lineto 38.85474 0.0 moveto 38.85474 4.25212 lineto 77.70947 0.0 moveto 77.70947 4.25212 lineto 116.56421 0.0 moveto 116.56421 4.25212 lineto 155.41895 0.0 moveto 155.41895 4.25212 lineto 194.27368 0.0 moveto 194.27368 4.25212 lineto 0.0 161.39484 moveto 0.0 157.14268 lineto 38.85474 161.39484 moveto 38.85474 157.14268 lineto 77.70947 161.39484 moveto 77.70947 157.14268 lineto 116.56421 161.39484 moveto 116.56421 157.14268 lineto 155.41895 161.39484 moveto 155.41895 157.14268 lineto 194.27368 161.39484 moveto 194.27368 157.14268 lineto pgfstr 0 TeXcolorgray restore restore save -141.7625 0.0 moveto -141.7625 161.39484 lineto 336.03618 161.39484 lineto 336.03618 0.0 lineto clip newpath save 0.19925 pgfw 0.5 TeXcolorgray 0.0 0.0 moveto 4.25266 0.0 lineto 0.0 53.79828 moveto 4.25266 53.79828 lineto 0.0 107.59656 moveto 4.25266 107.59656 lineto 0.0 161.39484 moveto 4.25266 161.39484 lineto 194.27368 0.0 moveto 190.021 0.0 lineto 194.27368 53.79828 moveto 190.021 53.79828 lineto 194.27368 107.59656 moveto 190.021 107.59656 lineto 194.27368 161.39484 moveto 190.021 161.39484 lineto pgfstr 0 TeXcolorgray restore restore 0.0 0.0 moveto 0.0 161.39484 lineto 194.27368 161.39484 lineto 194.27368 0.0 lineto 0.0 0.0 lineto closepath pgfstr save save [1.0 0.0 0.0 1.0 -2.49069 -9.94025 ] concat pgfs 1870 2399 a 0 setgray 1870 2399 a FE(0)1870 2399 y pgfr restore restore save save [1.0 0.0 0.0 1.0 22.49338 -11.62952 ] concat pgfs 1870 2399 a 0 setgray 1870 2399 a FE(2)18 b FB(\004)h FE(10)2056 2369 y Fx(\001)p FG(2)1870 2399 y pgfr restore restore save save [1.0 0.0 0.0 1.0 61.34811 -11.62952 ] 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