Stochastic Analysis (Translations of Mathematical Monographs)

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. Stochastic analysis is the analysis of functionals defined on the Wiener space, i.e., the space on which a Wiener process is realized. Since the Wiener space is infinite-dimensional, it requires a special calculus, the so-called Malliavin calculus. The goal of the book is to provide the reader with a concise introduction to stochastic analysis, and, in particular, to the Malliavin calculus. The book contains a detailed description of all 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.

this Book Offers A Concise Introduction To Stochastic Analysis, Particularly The Malliavin Calculus. A Detailed Description Is Given Of All Technical Tools Necessary To Describe The Theory, Such As The Wiener Process, The Ornstein-uhlenbeck Process, And Sobolev Spaces. Applications Of Stochastic Calculus To The Study Of Stochastic Differential Equations Are Also Presented. Chapter Exercises, Solutions, And Summaries Are Included. The Book Was Originally Published In Japanese By Iwanami Shoten, Publishers, Tokyo, 1998. The Author Is Also The Translator. Annotation © 2004 Book News, Inc., Portland, Or