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

 Part I. The Fundamental Principles: 1. Preface 2. Martingales 3. Fourier and Laplace transformations 4. Abstract WienerFrechet spaces 5. Two concepts of noanticipation in time 6. Malliavin calculus on the space of real sequences 7. Introduction to polysaturated models of mathematics 8. Extension of the real numbers and properties 9. Topology 10. Measure and integration on Loeb spaces Part II. An Introduction to Finite and InfiniteDimensional Stochastic Analysis: 11. From finite to infinitedimensional Brownian motion 12. The Ito integral for infinitedimensional Brownian motion 13. The iterated integral 14. Infinitedimensional OrnsteinUhlenbeck processes 15. Lindstrom's construction of standard Levy processes from discrete ones 16. Stochastic integration for Levy processes Part III. Malliavin Calculus: 17. Chaos decomposition 18. The Malliavin derivative 19. The Skorokhod integral 20. The interplay between derivative and integral 21. Skorokhod integral processes 22. Girsanov transformation 23. Malliavin calculus for Levy processes Appendix A. Polysaturated models Appendix B. The existence of polysaturated models References Index.
 (source: Nielsen Book Data)
 Publisher's 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, Levy 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.
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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 (hbk.)
 1107016142 (hbk.)