Malliavin Calculus with Applications to Stochastic Partial Differential Equations: 1st Edition (e-Book) book cover

Malliavin Calculus with Applications to Stochastic Partial Differential Equations

1st Edition

By Marta Sanz-Sole

EPFL Press

150 pages

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eBook (VitalSource) : 9780429104312
pub: 2005-08-17
from $28.98


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Description

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.

This book present

Table of Contents

Introduction. Integration by Parts and Absolute Continuity of Probability Laws. Finite Dimensional Malliavin Calculus. The Basic Operators of Malliavin Calculus. Representation of Wiener Functionals. Criteria for Absolute Continuity and Smoothness of Probability Laws. Stochastic Partial Differential Equations driven by Spatially Homogenous Gaussian Noise. Malliavin Regularity of Solutions of SPDEs. Analysis of the Malliavin Matrix of Solutions of SPDEs. Definition of Spaces Used Throughout the Course.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT007000
MATHEMATICS / Differential Equations
MAT037000
MATHEMATICS / Functional Analysis