An
Introduction to Infinite-Dimensional Analysis
Prato, Giuseppe Da.
creator
author.
aut
http://id.loc.gov/vocabulary/relators/aut
SpringerLink (Online service)
text
gw
2006
monographic
eng
access
X, 208 p. online resource.
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.
Gaussian measures in Hilbert spaces -- The Cameron–Martin formula -- Brownian motion -- Stochastic perturbations of a dynamical system -- Invariant measures for Markov semigroups -- Weak convergence of measures -- Existence and uniqueness of invariant measures -- Examples of Markov semigroups -- L2 spaces with respect to a Gaussian measure -- Sobolev spaces for a Gaussian measure -- Gradient systems.
by Giuseppe Da Prato.
Functional analysis
Distribution (Probability theory
Differential equations, partial
Functional Analysis
Probability Theory and Stochastic Processes
Partial Differential Equations
QA319-329.9
515.7
Springer eBooks
Universitext
9783540290216
https://doi.org/10.1007/3-540-29021-4
https://doi.org/10.1007/3-540-29021-4
ISI Library, Kolkata
100301
20181204131311.0
978-3-540-29021-6