Stochastic analysis
著者
書誌事項
Stochastic analysis
（Translations of mathematical monographs, v. 224）（Iwanami series in modern mathematics）
American Mathematical Society, c2004
- : pbk
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確率解析
Kakuritsu kaiseki
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注記
Originally published: Tokyo : Iwanami Shoten, 1998
Includes bibliographical references (p. 179-180) and index
内容説明・目次
内容説明
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.
目次
Wiener space Orenstein-Uhlenbeck process The Littlewood-Paley-Stein 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.
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