Limit Theorems for Stochastic Processes

  • Jean Jacod
  • Albert N. Shiryaev

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 288)

Table of contents

  1. Front Matter
    Pages I-XX
  2. Jean Jacod, Albert N. Shiryaev
    Pages 142-226
  3. Jean Jacod, Albert N. Shiryaev
    Pages 227-283
  4. Jean Jacod, Albert N. Shiryaev
    Pages 284-323
  5. Jean Jacod, Albert N. Shiryaev
    Pages 324-388
  6. Jean Jacod, Albert N. Shiryaev
    Pages 389-455
  7. Jean Jacod, Albert N. Shiryaev
    Pages 456-520
  8. Jean Jacod, Albert N. Shiryaev
    Pages 521-591
  9. Jean Jacod, Albert N. Shiryaev
    Pages 592-628
  10. Back Matter
    Pages 629-664

About this book

Introduction

Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.

Keywords

Convergence of processes Martingale Semimartingale Semimartingales Stochastic integrals Stochastic processes absolute continuity central limit theorem contiguity diffusion process random measure statistics stochastic process

Authors and affiliations

  • Jean Jacod
    • 1
  • Albert N. Shiryaev
    • 2
  1. 1.Laboratoire de ProbabilitésUniversité Paris VIParis Cedex 05France
  2. 2.Russian Academy of SciencesSteklov Mathematical InstituteMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-05265-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07876-7
  • Online ISBN 978-3-662-05265-5
  • Series Print ISSN 0072-7830
  • About this book