Malliavin Calculus with Applications to Stochastic Partial Differential Equations

Name: Malliavin Calculus with Applications to Stochastic Partial Differential Equations
Brand: EPFL Press English Imprint
SKU: 9782940222063
Price: 100.0 CHF
Availability: InStock
ISBN: 978-2-94022-206-3

de Marta Sanz-Solé (auteur)

Collection : Mathematics

avril 2005

Livre papier

format 160 x 240 178 pages En stock

88,15 €

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Présentation

Malliavin calculus is a stochastic calculus of variations on the Wiener space. The main results of this theory are currently having influence on research developments at the cross section of probability and infinite-dimensional analysis. On the applied level, Malliavin calculus is used, for example, in the study by probabilistic methods of mathematical models in finance. This book presents some applications of Malliavin calculus to stochastic partial differential equations driven by Gaussian noises. The first five chapters are devoted to an introduction of the calculus itself, based on a general Gaussian space. In the last chapters of the book, recent research on regularity of the solution of stochastic partial differential equations, and the existence and smoothness of their probability laws, are discussed.

Sommaire

Introduction
Integration by Parts and Absolute Continuity of Probability Laws
Finite Dimensional Malliavin Calculus
The Basic Operators of Malliavin Calculus
Representation of Wiener Functionals
_x0003_Criteria for Absolute Continuity
Stochastic Partial Differential Equations Driven by Spatially Homogeneous Gaussian Noise
Malliavin Regularity of Solutions of SPDE's
Analysis of the Malliavin Matrix of Solutions of the SPDE's
Definitions of spaces
Bibliography.