The Malliavin calculus and related topics / David Nualart.
Readers are assumed to have a firm grounding in probability as might be gained from a graduate course in the subject. Exercises at the end of each chapter help to reinforce a reader's understanding and to extend some of the ideas covered, and each chapter ends with a discussion of further direc...
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| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
New York :
Springer-Verlag,
[1995]
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| Series: | Probability and its applications (Springer-Verlag)
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| Subjects: |
| Summary: | Readers are assumed to have a firm grounding in probability as might be gained from a graduate course in the subject. Exercises at the end of each chapter help to reinforce a reader's understanding and to extend some of the ideas covered, and each chapter ends with a discussion of further directions that research has taken. The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space. Originally, it was developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems. This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus. The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hormander's theorem. Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions. |
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| Physical Description: | 1 online resource (xi, 266 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 241-260) and indexes. |
| ISBN: | 9781475724370 1475724373 9781475724394 147572439X |