Stochastic Calculus of Variations: For Jump Processes

Yasushi Ishikawa

Published by De Gruyter 2023

Stochastic Calculus of Variations

For Jump Processes

Yasushi Ishikawa

Volume 54 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110675290

Overview
Contents

About this book

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.

Author / Editor information

Yasushi Ishikawa, Ehime University, Japan.

Topics

Frontmatter Publicly Available Download PDF	I
Preface to the first edition Yasushi Ishikawa Publicly Available Download PDF	V
Preface to the second edition Yasushi Ishikawa Publicly Available Download PDF	VII
Preface to the third edition Yasushi Ishikawa Publicly Available Download PDF	IX
Contents Publicly Available Download PDF	XI
0 Introduction Requires Authentication Unlicensed Licensed Download PDF	1
1 Lévy processes and Itô calculus Requires Authentication Unlicensed Licensed Download PDF	5
2 Perturbations and properties of the probability law Requires Authentication Unlicensed Licensed Download PDF	47
3 Analysis of Wiener–Poisson functionals Requires Authentication Unlicensed Licensed Download PDF	146
4 Applications Requires Authentication Unlicensed Licensed Download PDF	265
A Appendix Requires Authentication Unlicensed Licensed Download PDF	335
Bibliography Requires Authentication Unlicensed Licensed Download PDF	347
List of symbols Requires Authentication Unlicensed Licensed Download PDF	357
Index Requires Authentication Unlicensed Licensed Download PDF	359

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 3rd ed.
Audience: Advanced Master and PhD students, researchers in Mathematics; academic libraries.
Pages
- Front matter: 14
- Main content: 362
Illustrations
- Illustrations: 7
Keywords: Malliavin calculus; Stochastic calculus; Stochastic functional differential equation; Stochastic partial differential equation

eBook

Published: July 24, 2023
ISBN: 9783110675290

Hardcover

Published: July 24, 2023
ISBN: 9783110675283