Malliavin Calculus for Levy Processes and Infinite-Dimensional Brownian Motion

Malliavin Calculus for Levy Processes and Infinite-Dimensional Brownian Motion
Author :
Publisher :
Total Pages : 430
Release :
ISBN-10 : 113923384X
ISBN-13 : 9781139233842
Rating : 4/5 (842 Downloads)

Book Synopsis Malliavin Calculus for Levy Processes and Infinite-Dimensional Brownian Motion by : Horst Osswald

Download or read book Malliavin Calculus for Levy Processes and Infinite-Dimensional Brownian Motion written by Horst Osswald and published by . This book was released on 2014-05-14 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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