An Introduction to Infinite-Dimensional Analysis
- Author
- Giuseppe Prato
- Publication Year
- 2006
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
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.
Keywords: Mathematics and Statistics / Brownian motion / Gaussian measures / Hilbert space / Markov processes / Probability theory / Sobolev space / White noise /functional analysis /invariant measures / Measure theory
