Two-Parameter Martingales and Their Quadratic Variation

Peter Imkeller (auth.)9780387192338, 0-387-19233-6

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.

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Table of contents :
Introduction….Pages 1-22
Notations and conventions….Pages 23-27
Basics; processes depending on a parameter….Pages 28-65
Two-parameter processes….Pages 66-98
Jumps of martingales and their compensation….Pages 99-130
Quadratic variation and structure of martingales….Pages 131-168