An Introduction to Infinite-Dimensional Analysis

• Main Author: Prato, Giuseppe Da (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Subjects: Mathematics.; Functional analysis.; Partial differential equations.; Probabilities.; Functional Analysis.; Probability Theory and Stochastic Processes.; Partial Differential Equations.

In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert spac...

Table of Contents:

• Gaussian measures in Hilbert spaces
• The Cameron–Martin formula
• Brownian motion
• Stochastic perturbations of a dynamical system
• Invariant measures for Markov semigroups
• Weak convergence of measures
• Existence and uniqueness of invariant measures
• Examples of Markov semigroups
• L2 spaces with respect to a Gaussian measure
• Sobolev spaces for a Gaussian measure
• Gradient systems.