The Malliavin calculus and related topics / David Nualart.

Author
Nualart, David, 1951- [Browse]
Format
Book
Language
English
Published/​Created
New York : Springer-Verlag, ©1995.
Description
xi, 266 pages : illustrations ; 25 cm

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Lewis Library - Stacks QA274.2 .N83 1995 Browse related items Request

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    Summary note
    • Readers are assumed to have a firm grounding in probability as might be gained from a graduate course in the subject. Exercises at the end of each chapter help to reinforce a reader's understanding and to extend some of the ideas covered, and each chapter ends with a discussion of further directions that research has taken.
    • The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space. Originally, it was developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems. This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus. The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hormander's theorem. Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions.
    Bibliographic references
    Includes bibliographical references (p. [241]-260) and indexes.
    Contents
    • 1. Analysis on the Wiener space
    • 2. Smoothness of probability laws
    • 3. Anticipating stochastic calculus
    • 4. Transformations of the Wiener measure.
    ISBN
    • 038794432X ((acid-free paper))
    • 9780387944326 ((acid-free paper))
    LCCN
    94048195
    OCLC
    31754140
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