Stochastic Analysis
This book accounts in 5 independent parts, recent main developments of Stochastic Analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer
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Editors
S. S. Chern B. Eckmann P. de la Harpe H. Hironaka F. Hirzebruch N. Hitchin L. Hormander M.-A. Knus A. Kupiainen J. Lannes G. Lebeau M. Ratner D. Serre Ya.G. Sinai N. J. A. Sloane J.Tits M. Waldschmidt S. Watanabe Managing Editors
M. Berger J. Coates S.R.S. Varadhan
Springer-Verlag Berlin Heidelberg GmbH
Paul Malliavin
Stochastic Analysis
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Malliavin, Paul: Stochastic analysis / Paul Malliavin. (A series of comprehensive studies in mathematics; 313)
ISBN 978-3-642-15073-9
ISBN 978-3-642-15074-6 (eBook)
DOI 10.1007/978-3-642-15074-6
NE: Grundlehren der mathematischen Wissenschaften
Mathematics Subject Classification (1991): 31C15, 31C25, 31C45, 35Ho5, 46E35, 60G15, 60G35, 60G44, 6oG60, 60H05, 60Ho7, 60H15, 60H30, 60}45, 60}60
First Reprint
2002
ISSN 0072-7830 ISBN 978-3-642-15073-9 This work is subject to copyright. All rights are reserved. whether the whole or part of the material is concerned. specifically the rights of translation. reprinting. reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law.
© Springer- Verlag Berlin Heidelberg 1997
Originally published by Springer-Verlag Berlin Heidelberg New York in 1997 Softcover reprint of the hardcover 1st edition 1997 Cover design: MetaDesign plus GmbH, Berlin Typesetting: Typeset in If.TEX by Ingeborg jebram, Heiligkreuzsteinach, and reformatted by Kurt Mattes, Heidelberg, using the MathTime fonts and a Springer TEX macro-package SPIN: 10866791 41/3111-54321 Printed on acid-free paper
Preface
An appropriate coverage of the subjects contained in the five parts of this book would need several monographs. We hope that the global treatment presented here may emphasize some of their deep interactions. As far as possible we present self-contained proofs; we have also tried to produce a book that could be used in a graduate course. Our thread of Ariadne is the introduction into stochastic analysis of the methodology used in classical analysis and differential geometry. Our geometric point of view has obliged us to pay great attention to the foundations. On the other hand our notation, which follows the usual conventions, will allow an experienced worker to look directly at any section of this book, without spending time on the foundational sections. Each part is constructed according to the following format: a short introduction, a detailed table of contents at the beginning of each chapter of that part and a short note on the literature at the end of each part. The style of writing oscillates from one part to the next between that of a rather technical monograph in Part I
