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Iwanami Series in Modern Mathematics
Stochastic Analysis
Ichiro Shigekawa, Kyoto University, Japan
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Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
2004; 182 pp; softcover
Volume: 224
ISBN-10: 0-8218-2626-3
ISBN-13: 978-0-8218-2626-3
List Price: US$49 Member Price: US$39.20
Order Code: MMONO/224

Stochastic analysis is often understood as the analysis of functionals defined on the Wiener space, i.e., the space on which the Wiener process is realized. Since the Wiener space is infinite-dimensional, it requires a special calculus, the so-called Malliavin calculus.

This book provides readers with a concise introduction to stochastic analysis, in particular, to the Malliavin calculus. It contains a detailed description of all the technical tools necessary to describe the theory, such as the Wiener process, the Ornstein-Uhlenbeck process, and Sobolev spaces. It also presents applications of stochastic calculus to the study of stochastic differential equations. The volume is suitable for graduate students and research mathematicians interested in probability and random processes.

Graduate students and research mathematicians interested in probability and random processes.

Reviews

"The book is wonderfully organized ... clearly written ... should be a useful text for an informal seminar or course on these developments. ... Shigekawa is to be congratulated on writing a nice book and the AMS for bringing it out at a reasonable price."

-- Bulletin of the American Mathematical Society