Synopses & Reviews
This introduction to Malliavin's stochastic calculus of variations is suitable for graduate students and professional mathematicians. Author Denis R. Bell particularly emphasizes the problem that motivated the subject's development, with detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and descriptions of a variety of applications.
The first chapter covers enough technical background to make the subsequent material accessible to readers without specialized knowledge of stochastic analysis. Succeeding chapters examine the functional analytic and variational approaches (with extensive explorations of the work of Stroock and Bismut); and elementary derivation of Malliavin's inequalities and a discussion of the different forms of the theory; and the non-degeneracy of the covariance matrix under Hormander's condition. The text concludes with a brief survey of applications of the Malliavin calculus to problems other than Hormander's.
Synopsis
This volume provides an introduction to Malliavin's stochastic calculus of variations. Suitable both for graduate students and for professional mathematicians, it discusses the development of the subject as well as applications. Denis R. Bell is a Professor of Mathematics at the University of North Florida.
Synopsis
This introduction to Malliavin's stochastic calculus of variations emphasizes the problem that motivated the subject's development, with detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and descriptions of a variety of applications. 1987 edition.
Synopsis
This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.
Table of Contents
Preface
Introduction
1. Background material
2. The functional analytic approach
3. The variational approach
4. An elementary derivation of Malliavins inequalities
5. A discussion of the different forms of the theory
6. Non-degeneracy of the covariance matrix under Hörmanders condition
7. Some further applications of the Malliavin calculus
References
Index