ENGLISH

An Introduction to Infinite-Dimensional Analysis

By Giuseppe Da Prato

Book information

Publisher
Springer
Year
2006
ISBN
9783540290209, 3-540-29020-6
Open Library ID
OL9055955M
Language
english
Format
PDF
Filesize
2 MB (2226700 bytes)
Series
Universitext
Edition
1
Pages
215\215
Time added
2010-04-25 21:59:20

Description

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.

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