Malliavin Calculus for LÚvy Processes and Infinite-Dimensional Brownian Motion

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Cambridge University Press, 2012 - Mathematics - 407 pages
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, LÚvy 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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Part II An introduction to finite and infinitedimensional stochastic analysis
Part III Malliavin calculus
Appendices Existence ofpolysaturated models

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About the author (2012)

Horst Osswald is a Professor of Mathematics at Universitńt MŘnchen.

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