The Malliavin Calculus (Dover Books on Mathematics)

Book Details

• Author: Denis R. Bell

• Publisher: Dover

• Language: English

• ISBN: 9780486449944

• Cover: Paperback

• Pages: 128

• Release Date: 07-04-2006

• Dimensions: 8.5 x 5.5 x 0.4 inches

About the Book

An Introduction to Malliavin Calculus by Denis R. Bell offers a clear and accessible entry point into one of the most significant advances in stochastic analysis. Specifically designed for graduate students and professional mathematicians, this compact volume lays the groundwork for understanding Malliavin's stochastic calculus of variations—a powerful tool in modern probability theory and mathematical finance.

The author opens with a concise yet comprehensive chapter on the technical background necessary for readers unfamiliar with advanced stochastic analysis. From there, the book delves into two major approaches to the subject: the functional analytic method developed by Stroock and the variational method introduced by Bismut. Through detailed exposition and comparison, Bell explains how these frameworks intersect, diverge, and enrich our understanding of the field.

Key topics include:

• Malliavin’s inequalities and their derivation

• The structure and implications of the covariance matrix under Hörmander’s condition

• Application-driven discussions that go beyond classical problems to cover a broader spectrum of real-world mathematical challenges

Whether you're studying stochastic partial differential equations, probabilistic approaches to PDEs, or the underpinnings of modern quantitative finance, this book is an invaluable resource. Its clarity, precision, and insightful treatment of foundational theories make it a must-read for scholars and professionals alike.