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-XVII
  2. Jean Jacod, Albert N. Shiryaev
    Pages 129-190
  3. Jean Jacod, Albert N. Shiryaev
    Pages 191-247
  4. Jean Jacod, Albert N. Shiryaev
    Pages 248-287
  5. Jean Jacod, Albert N. Shiryaev
    Pages 288-347
  6. Jean Jacod, Albert N. Shiryaev
    Pages 348-414
  7. Jean Jacod, Albert N. Shiryaev
    Pages 415-479
  8. Jean Jacod, Albert N. Shiryaev
    Pages 480-534
  9. Jean Jacod, Albert N. Shiryaev
    Pages 535-571
  10. Back Matter
    Pages 572-604

About this book


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 elementary introduction to the main topics: theory of martingales and 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.


Martingal Martingale Semimartingal Semimartingale Variation diffusion process statistics stochastic processes

Authors and affiliations

  • Jean Jacod
    • 1
  • Albert N. Shiryaev
    • 2
  1. 1.Laboratoire de ProbabilitésParis 05France
  2. 2.Steklov Mathematical InstituteMoscowUSSR

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02516-1
  • Online ISBN 978-3-662-02514-7
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site