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
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.