Stochastic Analysis
Itô and Malliavin Calculus in Tandem

AUTHORS:
Hiroyuki Matsumoto, Aoyama Gakuin University, Japan
Setsuo Taniguchi, Kyushu University, Japan



Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.

• Develops the Itô and the Malliavin calculi in tandem
• Details foundations and applications of Stochastic calculus
• Provides a path space analysis point of view

Table of Contents

Preface
Frequently used notation
1. Fundamentals of continuous stochastic processes
2. Stochastic integrals and Itô's formula
3. Brownian motion and Laplacian
4. Stochastic differential equations
5. Malliavin calculus
6. Black-Scholes model
7. Semiclassical limit
Appendix
References
Subject index.



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