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Giuseppe Da Prato 
Introduction to Infinite-Dimensional Analysis [PDF ebook] 

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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.

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语言 英语 ● 格式 PDF ● ISBN 9783540290216 ● 出版者 Springer Berlin Heidelberg ● 发布时间 2006 ● 下载 6 时 ● 货币 EUR ● ID 6592811 ● 复制保护 Adobe DRM
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