Continuous Strong Markov Processes in Dimension One

A stochastic calculus approach

  • Authors
  • Sigurd Assing
  • Wolfgang M. Schmidt

Part of the Lecture Notes in Mathematics book series (LNM, volume 1688)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Sigurd Assing, Wolfgang M. Schmidt
    Pages 1-13
  3. Sigurd Assing, Wolfgang M. Schmidt
    Pages 15-25
  4. Sigurd Assing, Wolfgang M. Schmidt
    Pages 27-32
  5. Sigurd Assing, Wolfgang M. Schmidt
    Pages 33-52
  6. Sigurd Assing, Wolfgang M. Schmidt
    Pages 53-77
  7. Sigurd Assing, Wolfgang M. Schmidt
    Pages 79-102
  8. Back Matter
    Pages 119-138

About this book

Introduction

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

Markov process Martingale Semimartingale Stochastic calculus calculus

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0096151
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-64465-1
  • Online ISBN 978-3-540-69786-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book