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Two-Parameter Martingales and Their Quadratic Variation

  • Book
  • © 1988

Overview

Authors:
  1. Peter Imkeller
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1308)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-IV
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  2. Introduction

    • Peter Imkeller
    Pages 1-22

  3. Notations and conventions

    • Peter Imkeller
    Pages 23-27

  4. Basics; processes depending on a parameter

    • Peter Imkeller
    Pages 28-65

  5. Two-parameter processes

    • Peter Imkeller
    Pages 66-98

  6. Jumps of martingales and their compensation

    • Peter Imkeller
    Pages 99-130

  7. Quadratic variation and structure of martingales

    • Peter Imkeller
    Pages 131-168

  8. Back Matter

    Pages 169-175
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Two-Parameter Martingales and Their Quadratic Variation

  • Authors: Peter Imkeller

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078096

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19233-6Published: 11 May 1988

  • eBook ISBN: 978-3-540-39148-7Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IV, 177

  • Topics: Probability Theory and Stochastic Processes

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