Introduction to Stochastic Analysis and Malliavin Calculus

• Main Author: Prato, Giuseppe Da (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2014.
• Series: Publications of the Scuola Normale Superiore ; 13
• Subjects: Mathematics.; Functional analysis.; Measure theory.; Probabilities.; Probability Theory and Stochastic Processes.; Functional Analysis.; Measure and Integration.

This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several...

Table of Contents:

• 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.