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Two-Parameter Martingales and Their Quadratic Variation

  • Authors
  • PeterĀ Imkeller

Part of the Lecture Notes in Mathematics book series (LNM, volume 1308)

Table of contents

  1. Front Matter
    Pages I-IV
  2. Peter Imkeller
    Pages 1-22
  3. Peter Imkeller
    Pages 23-27
  4. Peter Imkeller
    Pages 28-65
  5. Peter Imkeller
    Pages 66-98
  6. Peter Imkeller
    Pages 99-130
  7. Back Matter
    Pages 169-175

About this book

Introduction

This book has two-fold aims. In a first part it gives an introductory, thorough and essentially self-contained treatment of the general theory of two-parameter processes that has developed since around 1975. Apart from two survey papers by Merzbach and Meyer it is the first text of this kind. The second part presents the results of recent research by the author on martingale theory and stochastic calculus for two-parameter processes. Both the results and the methods of these two chapters are almost entirely new, and are of particular interest. They provide the fundamentals of a general stochastic analysis of two-parameter processes including, in particular, so far inaccessible jump phenomena. The typical rader is assumed to have some basic knowledge of the general theory of one-parameter martingales. The book should be accessible to probabilistically interested mathematicians who a) wish to become acquainted with or have a complete treatment of the main features of the general theory of two-parameter processes and basics of their stochastic calculus, b) intend to learn about the most recent developments in this area.

Keywords

Martingal Martingale Parameter Stochastic calculus Variation calculus quadratic variation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078096
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19233-6
  • Online ISBN 978-3-540-39148-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site