Translations of Mathematical Monographs Iwanami Series in Modern Mathematics 2004; 182 pp; softcover Volume: 224 ISBN10: 0821826263 ISBN13: 9780821826263 List Price: US$52 Member Price: US$41.60 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 infinitedimensional, it requires a special calculus, the socalled 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 OrnsteinUhlenbeck 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 "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  Wiener space
 OrensteinUhlenbeck process
 The LittlewoodPaleyStein inequality
 Sobolev spaces on an abstrct Wiener space
 Absolute continuity of distributions and smoothness of density functions
 Application to stochastic differential equations
 Perspectives on current research
 Bibliography
 Index
