Stochastic Calculus of Variations: For Jump Processes

✍ Scribed by Yasushi Ishikawa

• Publisher: De Gruyter
• Year: 2023
• Tongue: English
• Leaves: 376
• Series: De Gruyter Studies in Mathematics; 54
• Edition: 3rd ed.
• Category: Library

✦ Synopsis

This book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.

• Focuses on Malliavin calculus for jump processes.
• Includes many applications to control theory and mathematical finance.
• New in this edition: extensive updates and one novel application.

✦ Table of Contents

Preface to the first edition
Preface to the second edition
Preface to the third edition
Contents
0 Introduction
1 Lévy processes and Itô calculus
2 Perturbations and properties of the probability law
3 Analysis of Wiener–Poisson functionals
4 Applications
A Appendix
Bibliography
List of symbols
Index