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Limit Theorems for Stochastic Processes

  • Book
  • © 1987

Overview

Authors:
  1. Jean Jacod

    1. Laboratoire de Probabilités, Paris 05, France

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    You can also search for this author in PubMed   Google Scholar

  2. Albert N. Shiryaev

    1. Steklov Mathematical Institute, Moscow, USSR

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XVII
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  2. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals

    • Jean Jacod, Albert N. Shiryaev
    Pages 1-63

  3. Characteristics of Semimartingales and Processes with Independent Increments

    • Jean Jacod, Albert N. Shiryaev
    Pages 64-128

  4. Martingale Problems and Changes of Measures

    • Jean Jacod, Albert N. Shiryaev
    Pages 129-190

  5. Hellinger Processes, Absolute Continuity and Singularity of Measures

    • Jean Jacod, Albert N. Shiryaev
    Pages 191-247

  6. Contiguity, Entire Separation, Convergence in Variation

    • Jean Jacod, Albert N. Shiryaev
    Pages 248-287

  7. Skorokhod Topology and Convergence of Processes

    • Jean Jacod, Albert N. Shiryaev
    Pages 288-347

  8. Convergence of Processes with Independent Increments

    • Jean Jacod, Albert N. Shiryaev
    Pages 348-414

  9. Convergence to a Process with Independent Increments

    • Jean Jacod, Albert N. Shiryaev
    Pages 415-479

  10. Convergence to a Semimartingale

    • Jean Jacod, Albert N. Shiryaev
    Pages 480-534

  11. Limit Theorems, Density Processes and Contiguity

    • Jean Jacod, Albert N. Shiryaev
    Pages 535-571

  12. Back Matter

    Pages 572-604
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Keywords

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.

Authors and Affiliations

  • Laboratoire de Probabilités, Paris 05, France

    Jean Jacod

  • Steklov Mathematical Institute, Moscow, USSR

    Albert N. Shiryaev

Bibliographic Information

  • Book Title: Limit Theorems for Stochastic Processes

  • Authors: Jean Jacod, Albert N. Shiryaev

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-662-02514-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • eBook ISBN: 978-3-662-02514-7Published: 09 March 2013

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XVII, 604

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes

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