Document Zbl 1130.60064

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Dordrecht: Springer (ISBN 978-1-4020-5952-0/hbk; 978-90-481-7487-4/pbk; 978-1-4020-5953-7/ebook). xii, 228 p. (2007). </div> <div class="abstract">Recent developments of both, theory and practice, showed the necessity of using Itô stochastic differential equations for modelling complex dynamic and random phenomena in areas such as population biology, chemistry, physics, engineering and finance. Hence the need of having available appropriate textbooks. The author of this book has carefully selected and well described basic notions and concepts from probability theory and stochastic processes, all used later for building elements of stochastic analysis, or Itô stochastic integration and stochastic differential equations. The author’s approach, to follow a Hilbert space setting, allows him to explain well all notions and present basic results including some proofs. His goal is not to write about the most advanced achievements in this area, but rather to address the book to a wide category of readers, applied scientists, who need to use these sophisticated tools in their work. Most of the models are nonlinear stochastic differential equations, and very rarely their solutions can be explicitly expressed. Hence, we need a variety of approximate methods. This is one of the main goals of the author, to provide the reader with different approximate procedures/algorithms for solving stochastic equations, also discussing the accuracy. Statistical inference problems are briefly discussed. The next goal is to write about using Itô stochastic differential equations for modelling phenomena in biology, epidemiology, mechanics, physics, chemistry and finance.<br class="zbmathjax-paragraph">It is important to mention that all notions and results are well illustrated by appropriate examples. There are additional exercises (but no hints) and computer programs at the end of each chapter. The book ends with a very useful references list, a list of basic notations and a subject index. Besides researchers in the above mentioned areas, this book is suitable as a text for graduate university courses. I enjoyed reading the book and my expectation is that it will be met with interest by the readers.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A4356">Jordan M. Stoyanov (Newcastle upon Tyne)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A5129319">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A5129319">Cited in <strong>180</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A60H35" title="MSC2020">60H35</a> </td> <td class="space"> Computational methods for stochastic equations (aspects of stochastic analysis) </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 1130.60064" data-ciurl="/ci/05129319" data-biburl="/bibtex/05129319.bib" data-amsurl="/amsrefs/05129319.bib" data-xmlurl="/xml/05129319.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05129319.pdf" title="Zbl 1130.60064 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/10.1007/978-1-4020-5953-7" aria-label="DOI for “Modeling with Itô stochastic differential equations”" title="10.1007/978-1-4020-5953-7">DOI</a> </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 = ""; </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 ? 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