Introduction to stochastic analysis and Malliavin calculus / Giuseppe Da Prato.

Includes bibliographical references.

Introduction.-
1 Gaussian measures in Hilbert spaces.-
2 Gaussian random variables.-
3 The Malliavin derivative.-
4 Brownian Motion.-
5 Markov property of Brownian motion.-
6 Ito's integral.-
7 Ito's formula.-
8 Stochastic differential equations.-
9 Relationship between stochastic and parabolic equations.-
10 Formulae of Feynman-Kac and Girsanov.-
11 Malliavin calculus.-
12 Asymptotic behaviour of transition semigroups.-
A The Dynkin Theorem.-
B Conditional expectation.-
C Martingales.-
D Fixed points depending on parameters.-
E A basic ergodic theorem.-
References.

This book introduces differential stochastic equations and Malliavin calculus. The revised and expanded third edition offers corrections and improvements and a new section covering the differentiability of the Feynman-Kac semigroup.