Stochastic Analysis in Discrete and Continuous Settings

With Normal Martingales

  • Nicolas┬áPrivault

Part of the Lecture Notes in Mathematics book series (LNM, volume 1982)

Table of contents

  1. Front Matter
    Pages 1-7
  2. Nicolas Privault
    Pages 1-6
  3. Nicolas Privault
    Pages 7-58
  4. Nicolas Privault
    Pages 59-112
  5. Nicolas Privault
    Pages 113-130
  6. Nicolas Privault
    Pages 131-160
  7. Nicolas Privault
    Pages 161-194
  8. Nicolas Privault
    Pages 195-246
  9. Nicolas Privault
    Pages 247-280
  10. Nicolas Privault
    Pages 281-293
  11. Nicolas Privault
    Pages 295-300
  12. Back Matter
    Pages 1-15

About this book

Introduction

This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

Keywords

Brownian motion Malliavin calculus Martingale Normal martingales Poisson process Stochastic analysis continuous stochastic process jump process stochastic process

Authors and affiliations

  • Nicolas┬áPrivault
    • 1
  1. 1.Dept. MathematicsCity University of Hong KongHong KongHong Kong/PR China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-02380-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-02379-8
  • Online ISBN 978-3-642-02380-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book