Malliavin calculus for Lévy processes and infinitedimensional Brownian motion : an introduction
 Author/Creator
 Osswald, Horst.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2012, ©2012.
 Physical description
 xix, 407 pages : illustrations ; 24 cm.
 Series
 Cambridge tracts in mathematics ; 191.
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Available online

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QA274 .O87 2012

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QA274 .O87 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages 398403) and index.
 Contents

 Martingales
 Fourier and Laplace transformations
 Abstract WienerFréchet spaces
 Two concepts of noanticipation in time
 Malliavin calculus on the space of real sequences
 Introduction to polysaturated models of mathematics
 Extension of the real numbers
 Topology
 Measure and integration on Loeb spaces
 From finite to infinitedimensional Brownian motion
 The Itô integral for infinitedimensional Brownian motion
 Multiple integrals
 Infinitedimensional OrnsteinUhlenbeck processes
 Lindstrøm's construction of standard Lévy processes from discrete ones
 Stochastic integration for Lévy processes
 Chaos decomposition (for infinitedimensional Brownian motion)
 The Malliavin derivative
 The Skorohod integral
 The interplay between derivative and integral
 Skorohod integral processes
 Girsanov transformations
 Malliavin calculus for Lévy processes (Chaos, Malliavin derivative, ClarkOcone formula, Skorohod integral processes, Smooth representations, a communication rule for derivative and limit, product, chainrule, Girsanov transformations)
 Polysaturated models
 The existence of polysaturated models.
 Summary
 "Assuming only basic knowledge of probability theory and functional analysis, this book provides a selfcontained introduction to Malliavin calculus and infinitedimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinitedimensional problems to be treated as finitedimensional. 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, OrnsteinUhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, ClarkOcone 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" Provided by publisher.
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Contributor biographical information
Publisher description
Table of contents only
Subjects
Bibliographic information
 Publication date
 2012
 Copyright date
 2012
 Responsibility
 Horst Osswald.
 Series
 Cambridge tracts in mathematics ; 191
 ISBN
 9781107016149
 1107016142