Elements of Stochastic Calculus and Analysis

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Elements of Stochastic Calculus and Analysis is written by Daniel W. Stroock and published by Springer. It's available with International Standard Book Number or ISBN identification 3319770381 (ISBN 10) and 9783319770383 (ISBN 13).

This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material coveredhere has appeared in other places, this book attempts to explain the core ideas on which that material is based. As a consequence, the presentation is more an extended mathematical essay than a ``definition,lemma, theorem'' text. In addition, it includes several topics that are not usually treated elsewhere. For example,Wiener's theory of homogeneous chaos is discussed, Stratovich integration is given a novel development and applied to derive Wong and Zakai's approximation theorem, and examples are given of the application ofMalliavin's calculus to partial differential equations. Each chapter concludes with several exercises, some of which are quite challenging. The book is intended for use by advanced graduate students and researchmathematicians who may be familiar with many of the topics but want to broaden their understanding of them.