ENGLISH

The Malliavin calculus and related topics

By David Nualart

Book information

Publisher
Springer-Verlag
Year
1995
ISBN
9780387944326, 0-387-94432-X
LCC
QA274.2 .N83 1995
Open Library ID
OL1121430M
Language
english
Format
PDF
Filesize
3 MB (3367926 bytes)
Series
Probability and its applications
Edition
1
Pages
426\426
Library
mexmat
Time added
2009-07-20 03:45:11

Description

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. 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.

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