Elements of Stochastic Calculus and Analysis

Daniel W. Stroock

ISBN 10: 3030083543 / ISBN 13: 9783030083540

Published by Springer International Publishing, Springer International Publishing, 2019

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783030083540

Bibliographic Details

• Title: Elements of Stochastic Calculus and Analysis
• Publisher: Springer International Publishing, Springer International Publishing
• Publication Date: 2019
• Language: English
• ISBN 10: 3030083543
• ISBN 13: 9783030083540
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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.

About the Author

Daniel W. Stroock is Professor Emeritus of Mathematics at MIT. Professor Stroock's research interests focus on probability theory and stochastic processes.  Stroock (with S. Varadhan) was awarded the Leroy P. Steele Prize for seminal contributions to research in stochastic equations. In 2007, Stroock received an Honorary Fellowship at Swansea University, Wales, and in 2004 selected to be Foreign Member of the Polish Academy of Arts and Sciences. Professor Stroock is a Fellow of the American Academy of Arts and Sciences (1991), and a Member of the National Academy of Sciences (1995). Professor Stroock has made many contributions to pedagogical literature, among these include: An Introduction to Markov Processes" (GTM 230),  "Essentials of Integration Theory for Analysis" (GTM 262), "Multidimensional Diffusion Processes" (Classics in Mathematics).