Stochastic Analysis

Itô and Malliavin Calculus in Tandem

AvHiroyuki Matsumoto,Setsuo Taniguchi

Inbunden, Engelska, 2016

Del 159 i serien Cambridge Studies in Advanced Mathematics

854 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-11-07
Mått:157 x 235 x 25 mm
Vikt:630 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:357
Förlag:Cambridge University Press
ISBN:9781107140516

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Mer om författaren

Hiroyuki Matsumoto is Professor of Mathematics at Aoyama Gakuin University. He graduated from Kyoto University in 1982 and received his doctor of science degree from Osaka University in 1989. His research focuses on stochastic analysis and its applications to spectral analysis of Schrödinger operations and Selberg's trace formula, and he has published several books in Japanese, including Stochastic Calculus and Introduction to Probability and Statistics. He is a member of the Mathematical Society of Japan and an editor of the MSJ Memoirs. Setsuo Taniguchi is Professor of Mathematics at Kyushu University. He graduated from Osaka University in 1980 and received his doctor of science degree from Osaka University in 1989. His research interests include stochastic differential equations and Malliavin calculus. He has published several books in Japanese, including Introduction to Stochastic Analysis for Mathematical Finance and Stochastic Calculus. He is a member of the Mathematical Society of Japan and is an editor of the Kyushu Journal of Mathematics.

Recensioner i media

'This book is a comprehensive guide to stochastic analysis related to Brownian motion. It contains the basis of the Itô calculus and the Malliavin calculus, which are the heart of the modern analysis of Brownian motion. The book is self-contained and it is accessible for graduate students and researchers who wish to learn about stochastic differential equations.' Hiroshi Kunita

Innehållsförteckning

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.