**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2004; 182 pp; Softcover

MSC: Primary 60;

**Print ISBN: 978-0-8218-2626-3**

Product Code: MMONO/224

Product Code: MMONO/224

List Price: $52.00

AMS Member Price: $41.60

MAA Member Price: $46.80

**Electronic ISBN: 978-1-4704-4648-2
Product Code: MMONO/224.E**

List Price: $52.00

AMS Member Price: $41.60

MAA Member Price: $46.80

# Stochastic Analysis

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*Ichiro Shigekawa*

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.

#### Readership

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

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Stochastic Analysis

- Cover Cover11
- Title page i2
- Contents iii4
- Preface to the English edition v6
- Preface to the Japanese edition vii8
- Outline of the theory and the objectives ix10
- Wiener space 114
- Orenstein-Uhlenbeck process 2134
- The Littlewood-Paley-Stein inequality 4760
- Sobolev spaces on an abstract Wiener space 7992
- Absolute continuity of distributions and smoothness of density functions 103116
- Application to stochastic differential equations 121134
- Perspectives on current research 175188
- Bibliography 179192
- Index 181194
- Back Cover Back Cover1198