This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material covered
here 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 of
Malliavin'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 research
mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.
Before he retired, Stroock had been on the faculty of several universities, most recently M.I.T. The majority of his work has to do with analytic aspects of probability theory, especially the application of probability theory to partial differential equations. He is a member of the American Mathematical Society, the American Academy of Arts and Sciences, the National Academy of Sciences, and the Polish Academy of Arts and Sciences.
Περιγραφή
This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material covered
here 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 of
Malliavin'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 research
mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.
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