Document Zbl 1328.62291

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World J., Probab. Stat.</a> <a href="/?q=in%3A351393" title="Articles in this Issue">2014, Article ID 589167, 9 p. (2014)</a>. </div> <div class="abstract">Summary: This paper is concerned with the convergence of stochastic $\theta$-methods for stochastic pantograph equations with Poisson-driven jumps of random magnitude. The strong order of the convergence of the numerical method is given, and the convergence of the numerical method is obtained. Some earlier results are generalized and improved.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G30" title="MSC2020">62G30</a> </td> <td class="space"> Order statistics; empirical distribution functions </td> </tr></table> </div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1328.62291" data-ciurl="/ci/06529679" data-biburl="/bibtex/06529679.bib" data-amsurl="/amsrefs/06529679.bib" data-xmlurl="/xml/06529679.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06529679.pdf" title="Zbl 1328.62291 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1155/2014/589167" aria-label="DOI for “Stochastic $\theta$-methods for a class of jump-diffusion stochastic pantograph equations with random magnitude”" title="10.1155/2014/589167">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">X. 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Wu, “A note on order of convergence of numerical method for neutral stochastic functional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 3, pp. 1194-1200, 2012. · <a href="/1257.65005" class="nowrap">Zbl 1257.65005</a> · <a href="https://doi.org/10.1016/j.cnsns.2011.08.013" class="nowrap">doi:10.1016/j.cnsns.2011.08.013</a></td> </tr><tr> <td>[20]</td> <td class="space">A. Gardoń, “The order of approximations for solutions of Itô-type stochastic differential equations with jumps,” Stochastic Analysis and Applications, vol. 22, no. 3, pp. 679-699, 2004. · <a href="/1056.60065" class="nowrap">Zbl 1056.60065</a> · <a href="https://doi.org/10.1081/SAP-120030451" class="nowrap">doi:10.1081/SAP-120030451</a></td> </tr><tr> <td>[21]</td> <td class="space">P. Hu and C. Huang, “Stability of stochastic \theta -methods for stochastic delay integro-differential equations,” International Journal of Computer Mathematics, vol. 88, no. 7, pp. 1417-1429, 2011. · <a href="/1222.65010" class="nowrap">Zbl 1222.65010</a> · <a href="https://doi.org/10.1080/00207160.2010.509430" class="nowrap">doi:10.1080/00207160.2010.509430</a></td> </tr><tr> <td>[22]</td> <td class="space">X. Mao and S. Sabanis, “Numerical solutions of stochastic differential delay equations under local Lipschitz condition,” Journal of Computational and Applied Mathematics, vol. 151, no. 1, pp. 215-227, 2003. · <a href="/1015.65002" class="nowrap">Zbl 1015.65002</a> · <a href="https://doi.org/10.1016/S0377-0427(02)00750-1" class="nowrap">doi:10.1016/S0377-0427(02)00750-1</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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