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Introduction to Infinite-Dimensional Analysis

Name: Introduction to Infinite-Dimensional Analysis
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 05273814
Price: 20202 HUF
Availability: InStock
Author: Giuseppe Da Prato
ISBN: 9783540290209

Giuseppe Da Prato

Language

English

Book Hardback

Libristo code: 05273814

Publishers Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, July 2006

In this revised and extended version of his course notes from a 1-year course at Scuola Normale Supe... Full description

Libristo code: 05273814

133 b

20 202 Ft

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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 space of infinite dimension. Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way.§These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.