Stochastic Analysis: Itô and Malliavin Calculus in Tandem (Cambridge Studies in Advanced Mathematics, Series Number 159)

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 Fundamentals Of Continuous Stochastic Processes -- Stochastic Integrals And Itô's Formula -- Brownian Motion And The Laplacian -- Stochastic Differential Equations -- Malliavin Calculus -- The Black-scholes Model -- The Semiclassical Limit -- Appendix. Some Fundamentals. Hiroyuki Matsumoto (aoyama Gakuin University, Japan), Setsuo Taniguchi (kyushu University, Japan). Includes Bibliographical References (pages 337-343) And Index. Translated And Adapted From The Japanese Edition. Content: Preface Frequently used notation 1. Fundamentals of continuous stochastic processes 2. Stochastic integrals and Ito'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. This compact, graduate-level text develops the Ito calculus and the Malliavin calculus in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance, and taking readers from foundations to current, groundbreaking applications.