European Mathematical Society - t. g. kurtz
https://euro-math-soc.eu/author/t-g-kurtz
enLarge Deviations for Stochastic Processes
https://euro-math-soc.eu/review/large-deviations-stochastic-processes
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is focused on recent results on large deviation for a general class of Markov processes obtained mostly by the authors. It is not intended for beginners and inexperienced readers and a very good mathematical background and a preliminary knowledge of Markov processes and stochastic analysis is an advantage when reading the book. The volume itself is divided into five parts. The book starts with an introduction and overview with many motivating examples and it ends with an extensive appendix containing useful results on operators, semigroups and mass transport theory. The core of the book is in the remaining three sections. Large deviations in general are treated in section 1. The exponential tightness and necessary and sufficient conditions for it are given in an analogous way as for classical tightness of measures. The rate function is introduced and the problem of identifying the rate function is studied. Section 2 gives an overview of the classical semigroup approach to large deviations of Markov processes and an alternative approach using viscosity solutions. The proofs of large deviation results need verification of a comparison principle. Since it is typically the most difficult step, a chapter in section 3 is devoted to this problem. In the rest of section 3, the comparison principle is discussed for different stochastic processes, in particular for nearly deterministic processes with almost negligible perturbation, for stochastic processes in a random environment, for occupation measures of Markov processes and, finally, for solutions of stochastic equations in infinite dimensions. Large deviations have many applications in probability and statistics, hence the book may be recommended to researchers in the field of stochastic processes and their applications or to specialists in statistics of stochastic processes.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">dhl</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/j-feng" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">j. feng</a></li><li class="vocabulary-links field-item odd"><a href="/author/t-g-kurtz" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">t. g. kurtz</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/american-mathematical-society" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2006</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-8218-4145-7 </div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 99</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/60-probability-theory-and-stochastic-processes" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">60 Probability theory and stochastic processes</a></li></ul></span>Sat, 14 May 2011 12:22:39 +0000Anonymous39065 at https://euro-math-soc.eu