The Malliavin Calculus
β Denis R. Bell
π Library
π
2006
π Dover Publications, Inc.
π English
β¦ LIBER β¦
π
The Malliavin calculus
β Scribed by Denis R. Bell
- Publisher
- Longman Higher Education
- Year
- 1987
- Tongue
- English
- Leaves
- 115
- Series
- Pitman Monographs & Surveys in Pure & Applied Mathematics 34
- Edition
- 1st
- Category
- Library
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β¦ Synopsis
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.
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.
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This book is a unique and profound contribution to the investigation of diffusion processes and stochastic analysis on manifolds. It employs the M alliavin calculus and large deviation techniques to study the asymptotics of the conditional probabilities of bridges associated with certain
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From the reviews "This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. The high quality of this work [...] makes a fascinating subject and its open p