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Stochastic Analysis

Ichiro Shigekawa Kyoto University, Kyoto, Japan
Available Formats:
Softcover ISBN: 978-0-8218-2626-3
Product Code: MMONO/224
List Price: $52.00 MAA Member Price:$46.80
AMS Member Price: $41.60 Electronic ISBN: 978-1-4704-4648-2 Product Code: MMONO/224.E List Price:$52.00
MAA Member Price: $46.80 AMS Member Price:$41.60
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List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Click above image for expanded view Stochastic Analysis Ichiro Shigekawa Kyoto University, Kyoto, Japan Available Formats:  Softcover ISBN: 978-0-8218-2626-3 Product Code: MMONO/224  List Price:$52.00 MAA Member Price: $46.80 AMS Member Price:$41.60
 Electronic ISBN: 978-1-4704-4648-2 Product Code: MMONO/224.E
 List Price: $52.00 MAA Member Price:$46.80 AMS Member Price: $41.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
• Book Details

Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
Volume: 2242004; 182 pp
MSC: 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 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.

• Chapters
• Wiener space
• Orenstein-Uhlenbeck process
• The Littlewood-Paley-Stein 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

• 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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Iwanami Series in Modern Mathematics
Volume: 2242004; 182 pp
MSC: 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 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.

• Chapters
• Wiener space
• Orenstein-Uhlenbeck process
• The Littlewood-Paley-Stein 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
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