Skip to main content
SpringerLink
Log in

Transformation of Measure on Wiener Space

  • Book
  • © 2000

Overview

Authors:
  1. Ali Süleyman Üstünel

    1. Département Infres, Ecole Nationale Supérieure des Télécommunications, Paris, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Moshe Zakai

    1. Technion-Israel Institute of Technology, Faculty of Electrical Engineering, Haifa, Israel

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • No other book on this subject
  • Addresses fundamental problems and will be the standard reference for a long time to come
  • The authors have different scientific origins and combine these successfully in the comined authorship of this book
  • Includes supplementary material: sn.pub/extras

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIII
    Download chapter PDF

  2. Introduction

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 1-4

  3. Some Background Material and Preliminary Results

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 5-19

  4. Transformation of Measure Induced by Adapted Shifts

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 21-51

  5. Transformation of Measure Induced by General Shifts

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 53-98

  6. The Sard Inequality

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 99-113

  7. Transformation of Measure Under Anticipative Flows

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 115-156

  8. Monotone Shifts

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 157-180

  9. Generalized Radon-Nikodym Derivatives

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 181-205

  10. Random Rotations

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 207-231

  11. The Degree Theorem on Wiener Space

    • Ali Süleyman Üstünel, Moshe Zakai
    Pages 233-254

  12. Back Matter

    Pages 255-297
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Département Infres, Ecole Nationale Supérieure des Télécommunications, Paris, France

    Ali Süleyman Üstünel

  • Technion-Israel Institute of Technology, Faculty of Electrical Engineering, Haifa, Israel

    Moshe Zakai

Bibliographic Information

  • Book Title: Transformation of Measure on Wiener Space

  • Authors: Ali Süleyman Üstünel, Moshe Zakai

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-13225-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Hardcover ISBN: 978-3-540-66455-0Published: 29 November 1999

  • Softcover ISBN: 978-3-642-08572-7Published: 05 December 2010

  • eBook ISBN: 978-3-662-13225-8Published: 14 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XIII, 298

  • Topics: Measure and Integration, Functional Analysis, Probability Theory and Stochastic Processes

Publish with us

Policies and ethics

Back to top

Search

Navigation