TY - BOOK
AU - Prato,Giuseppe Da
ED - SpringerLink (Online service)
TI - An Introduction to Infinite-Dimensional Analysis
T2 - Universitext,
SN - 9783540290216
AV - QA319-329.9
U1 - 515.7 23
PY - 2006///
CY - Berlin, Heidelberg
PB - Springer Berlin Heidelberg
KW - Functional analysis
KW - Distribution (Probability theory
KW - Differential equations, partial
KW - Functional Analysis
KW - Probability Theory and Stochastic Processes
KW - Partial Differential Equations
N1 - 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
N2 - 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
UR - https://doi.org/10.1007/3-540-29021-4
ER -