The Malliavin Calculus and Related Topics

  • David Nualart

Part of the Probability and its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages i-xi
  2. David Nualart
    Pages 1-2
  3. David Nualart
    Pages 3-75
  4. David Nualart
    Pages 77-145
  5. David Nualart
    Pages 147-186
  6. David Nualart
    Pages 187-233
  7. Back Matter
    Pages 235-266

About this book

Introduction

The origin of this book lies in an invitation to give a series of lectures on Malliavin calculus at the Probability Seminar of Venezuela, in April 1985. The contents of these lectures were published in Spanish in [176]. Later these notes were completed and improved in two courses on Malliavin cal­ culus given at the University of California at Irvine in 1986 and at Ecole Polytechnique Federale de Lausanne in 1989. The contents of these courses correspond to the material presented in Chapters 1 and 2 of this book. Chapter 3 deals with the anticipating stochastic calculus and it was de­ veloped from our collaboration with Moshe Zakai and Etienne Pardoux. The series of lectures given at the Eighth Chilean Winter School in Prob­ ability and Statistics, at Santiago de Chile, in July 1989, allowed us to write a pedagogical approach to the anticipating calculus which is the basis of Chapter 3. Chapter 4 deals with the nonlinear transformations of the Wiener measure and their applications to the study of the Markov property for solutions to stochastic differential equations with boundary conditions.

Keywords

Markov property Stochastic calculus Variation calculus differential equation stochastic differential equation

Authors and affiliations

  • David Nualart
    • 1
  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2437-0
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-2439-4
  • Online ISBN 978-1-4757-2437-0
  • Series Print ISSN 1431-7028
  • About this book