Elements of Stochastic Calculus and Analysis

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