An Introduction to Analysis on Wiener Space
This book gives the basis of the probabilistic functional analysis on Wiener space, developed during the last decade. The subject has progressed considerably in recent years thr- ough its links with QFT and the impact of Stochastic Calcu- lus of Variation
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Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
Ali Stileyman Dstunel
An Introduction to Analysis on Wiener Space
Springer
Author Ali Siileyman Ustunel ENST, Dept. Reseaux 46, rue Barrault F-75013 Paris, France e-mail: [email protected]
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Usttinel, All Siileyman:
An introduction to analysis on Wiener space / Ali Suleyman Ustunel. - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Tokyo: Springer, 1995 (Lecture notes in mathematics; Vol 1610)
ISBN 3-540-60170-8 NE:GT
Mathematics Subject Classification (1991): 60H07, 60H05, 60H15, 46F25, 8IT, 81Q ISBN 3-540-60170-8 Springer-Verlag Berlin Heidelberg New York 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1995 Printed in Germany Typesetting: Camera-readyTj-X output by the author SPIN: 10479544 46/3142-543210 - Printed on acid-free paper
Ankara Fen Lisesi 67-70 mezunlarma .
Introduction The following pages are the notes from a seminar that I gave during the spring and some portion of the summer of 1993 at the Mathematics Institute of Oslo University. The aim of the seminars was to give a rapid but rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the impulse of the Stochastic Calculus of Variations of Paul Malliavin (cf. [12]). Although some concepts are in the preliminaries, I assumed that the students had already acquired the notions of stochastic calculus with semimartingales, Brownian motion and some rudiments of the theory of Markov processes. A small portion of the material exposed is our own research, in particular, with Moshe Zakai. The rest has been taken from the works listed in the bibliography. The first chapter deals with the definition of the (so-called) Gross-Sobolev derivative and the Ornstein-Uhlenbeck operator which are indispensable tools of the analysis on Wiener space. In the second chapter we begin the proof of the Meyer inequalities, for which the hypercontractivity property of the OrnsteinUhlenbeck semigroup is needed. We expose this last topic in the third chapter, then come back to Meyer inequalities, and complete their proof in chapter IV. Different applications are given in next two chapters. In the seventh chapter we study the independence of some Wiener functionals wi
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