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An Introduction to Infinite-Dimensional Analysis

An Introduction to Infinite-Dimensional Analysis - Universitext

2006

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Publisher's Synopsis

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.

Book information

ISBN: 9783642421686
Publisher: Springer Berlin Heidelberg
Imprint: Springer
Pub date:
Edition: 2006
Language: English
Number of pages: 208
Weight: 349g
Height: 235mm
Width: 155mm
Spine width: 12mm