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Continuous Strong Markov Processes in Dimension One

A Stochastic Calculus Approach

  • Book
  • © 1998

Overview

Authors:
  1. Sigurd Assing
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  2. Wolfgang M. Schmidt
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1688)

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About this book

The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.

Keywords

Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
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  2. Basic concepts and preparatory results

    • Sigurd Assing, Wolfgang M. Schmidt
    Pages 1-13

  3. Classification of the points of the state space

    • Sigurd Assing, Wolfgang M. Schmidt
    Pages 15-25

  4. Weakly additive functionals and time change of strong Markov processes

    • Sigurd Assing, Wolfgang M. Schmidt
    Pages 27-32

  5. Semimartingale decomposition of continuous strong Markov semimartingales

    • Sigurd Assing, Wolfgang M. Schmidt
    Pages 33-52

  6. Occupation time formula

    • Sigurd Assing, Wolfgang M. Schmidt
    Pages 53-77

  7. Construction of continuous strong Markov processes

    • Sigurd Assing, Wolfgang M. Schmidt
    Pages 79-102

  8. Continuous strong Markov semimartingales as solutions of stochastic differential equations

    • Sigurd Assing, Wolfgang M. Schmidt
    Pages 103-118

  9. Back Matter

    Pages 119-138
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Bibliographic Information

  • Book Title: Continuous Strong Markov Processes in Dimension One

  • Book Subtitle: A Stochastic Calculus Approach

  • Authors: Sigurd Assing, Wolfgang M. Schmidt

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096151

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-64465-1Published: 20 May 1998

  • eBook ISBN: 978-3-540-69786-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 140

  • Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods

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