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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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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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Keywords

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.

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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