Document Zbl 0744.60032

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New York etc: John Wiley & Sons, Inc. xiii, 672 p. (1990). </div> <div class="abstract">The authors describe the scope of the book in their preface as follows:<br class="zbmathjax-paragraph">“This is a text on stochastic processes for graduate students in science and engineering, including mathematics and statistics. In the main body of the text the theory is developed at a relatively simple technical level with some emphasis on computation and examples. Sometimes to make a mathematical argument complete, certain of the more technical explanations are relegated to the end of the chapter under the label theoretical complements. This approach also allows some flexibility in instruction. A few sample course outlines have been provided to illustrate the possibilities for designing various types of courses based on this book. The theoretical complements also contain some supplementary results and references to the literature.<br class="zbmathjax-paragraph">Measure theory is used sparingly and with explanation. The instructor may exercise control over its emphasis and use depending on the background of the majority of the students in the class.<br class="zbmathjax-paragraph">Chapter applications, appearing at the end of the chapters, are largely drawn from physics, computer science, economics, and engineering. There are many additional examples and applications illustrating the theory; they appear in the text and among the exercises.<br class="zbmathjax-paragraph">Some of the more advanced or difficult exercises are marked by asterisks. Many appear with hints. Some exercises are provided to complete an argument or statement in the text. Occasionally certain well-known results are only a few steps away from the theory developed in the text. Such results are often cited in the exercises, along with an outline of steps, which can be used to complete their derivation.”<br class="zbmathjax-paragraph">The chapter headlines are: Random walk and Brownian motion; Discrete- parameter Markov chains; Birth-death Markov chains; Continuous-parameter Markov chains; Brownian motion and diffusions; Dynamic programming and stochastic optimization; An introduction to stochastic differential equations; A probability and measure theory overview.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A47283">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A47283">Cited in <strong>95</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A60Gxx" title="MSC2020">60Gxx</a> </td> <td class="space"> Stochastic processes </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60Jxx" title="MSC2020">60Jxx</a> </td> <td class="space"> Markov processes </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60-01" title="MSC2020">60-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60H10" title="MSC2020">60H10</a> </td> <td class="space"> Stochastic ordinary differential equations (aspects of stochastic analysis) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A60Kxx" title="MSC2020">60Kxx</a> </td> <td class="space"> Special processes </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atext+on+stochastic+processes+for+graduate+students">text on stochastic processes for graduate students</a>; <a href="/?q=ut%3Aapplications">applications</a>; <a href="/?q=ut%3Arandom+walk">random walk</a>; <a href="/?q=ut%3ABrownian+motion">Brownian motion</a>; <a href="/?q=ut%3AMarkov+Chains">Markov Chains</a>; <a href="/?q=ut%3ADiffusions">Diffusions</a>; <a href="/?q=ut%3ADynamic+Programming">Dynamic Programming</a>; <a href="/?q=ut%3AStochastic+Optimization">Stochastic Optimization</a>; <a href="/?q=ut%3AStochastic+Differential+Equations">Stochastic Differential Equations</a></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 0744.60032" data-ciurl="/ci/00047283" data-biburl="/bibtex/00047283.bib" data-amsurl="/amsrefs/00047283.bib" data-xmlurl="/xml/00047283.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00047283.pdf" title="Zbl 0744.60032 as PDF">Review PDF</a> </div> <div class="fulltexts"> </div> <div class="sfx" style="float: right;"> </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 = ""; 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