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Book 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 details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Introduction to Infinite-Dimensional Analysis
• Author: Giuseppe Da Prato
• Language: English
• Binding: Hardback
• Number of pages: 208
• EAN: 9783540290209
• ISBN: 3540290206
• ID: 05273814
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 720 g
• Dimensions: 297 × 210 × 13 mm
• Date of publishing: 03. July 2006

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