Stochastic Analysis
Itô and Malliavin Calculus in Tandem

Developing the Itô calculus and Malliavin calculus in tandem, this book crystallizes modern day stochastic analysis into a single volume.

Hiroyuki Matsumoto (Author), Setsuo Taniguchi (Author)

9781107140516, Cambridge University Press

Hardback, published 7 November 2016

357 pages
23.5 x 15.7 x 2.5 cm, 0.63 kg

'This book develops stochastic analysis from the path space point of view, with an emphasis on the connection between Brownian motion and partial differential equations. A detailed treatment of Malliavin calculus and important applications in finance and physics make this monograph an innovative and useful reference in the field.' David Nualart, University of Kansas

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.

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.

Subject Areas: Stochastics [PBWL], Probability & statistics [PBT]