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.
| Autorius: | Giuseppe Da Prato |
| Serija: | Universitext |
| Leidėjas: | Springer Berlin Heidelberg |
| Išleidimo metai: | 2006 |
| Knygos puslapių skaičius: | 228 |
| ISBN-10: | 3540290206 |
| ISBN-13: | 9783540290209 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Functional analysis and transforms |
Parašykite atsiliepimą apie „An Introduction to Infinite-Dimensional Analysis“
