Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion (Cambridge Tracts in Mathematics) - Hardcover

Horst Osswald

 
9781107016149: Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion (Cambridge Tracts in Mathematics)
Hardcover
ISBN 10: 1107016142 ISBN 13: 9781107016149
Publisher: Cambridge University Press, 2012

Synopsis

Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Levy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques.

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About the Author

Horst Osswald is a Professor of Mathematics at Universitat Munchen.

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Publisher
Cambridge University Press
Publication date
2012
Language
English
ISBN 10 
1107016142
ISBN 13 
9781107016149
Binding
Hardcover
Number of pages
350