Softcover ISBN:  9780821826263 
Product Code:  MMONO/224 
182 pp 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $41.60 
Electronic ISBN:  9781470446482 
Product Code:  MMONO/224.E 
182 pp 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $41.60 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 224; 2004MSC: Primary 60;
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.ReadershipGraduate students and research mathematicians interested in probability and random processes.

Table of Contents

Chapters

Wiener space

OrensteinUhlenbeck process

The LittlewoodPaleyStein inequality

Sobolev spaces on an abstract Wiener space

Absolute continuity of distributions and smoothness of density functions

Application to stochastic differential equations

Perspectives on current research


Additional Material

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


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

Chapters

Wiener space

OrensteinUhlenbeck process

The LittlewoodPaleyStein inequality

Sobolev spaces on an abstract Wiener space

Absolute continuity of distributions and smoothness of density functions

Application to stochastic differential equations

Perspectives on current research

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