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Transformation of Measure on Wiener Space

  • Ali Süleyman Üstünel
  • Moshe Zakai

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Ali Süleyman Üstünel, Moshe Zakai
    Pages 1-4
  3. Ali Süleyman Üstünel, Moshe Zakai
    Pages 5-19
  4. Ali Süleyman Üstünel, Moshe Zakai
    Pages 21-51
  5. Ali Süleyman Üstünel, Moshe Zakai
    Pages 53-98
  6. Ali Süleyman Üstünel, Moshe Zakai
    Pages 99-113
  7. Ali Süleyman Üstünel, Moshe Zakai
    Pages 115-156
  8. Ali Süleyman Üstünel, Moshe Zakai
    Pages 157-180
  9. Ali Süleyman Üstünel, Moshe Zakai
    Pages 181-205
  10. Ali Süleyman Üstünel, Moshe Zakai
    Pages 207-231
  11. Ali Süleyman Üstünel, Moshe Zakai
    Pages 233-254
  12. Back Matter
    Pages 255-297

About this book

Introduction

This book gives a systematic presentation of the main results on the transformation of measure induced by shift transformations on Wiener space. This topic has its origins in the work of Cameron and Martin (anticipative shifts, 1940's) and that of Girsanov (non-anticipative shifts, 1960's). It played an important role in the development of non-anticipative stochastic calculus and itself developed under the impulse of the stochastic calculus of variations. The recent results presented in the book include a dimension-free form of the Girsanov theorem, the transformations of measure induced by anticipative non-invertible shift transformations, the transformation of measure induced by flows, the extension of the notions of Sard lemma and degree theory to Wiener space, generalized distribution valued Radon-Nikodym theorems and measure preserving transformations. Basic probability theory and the Ito calculus are assumed known; the necessary results from the Malliavin calculus are presented in the appendix. Aimed at graduate students and researchers, it can be used as a text for a course or a seminar.

Keywords

Derivative Probability theory Stochastic calculus abstract Wiener space calculus functional analysis measure

Authors and affiliations

  • Ali Süleyman Üstünel
    • 1
  • Moshe Zakai
    • 2
  1. 1.Département InfresEcole Nationale Supérieure des TélécommunicationsParisFrance
  2. 2.Technion-Israel Institute of TechnologyFaculty of Electrical EngineeringHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-13225-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08572-7
  • Online ISBN 978-3-662-13225-8
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site