An Introduction to Infinite-Dimensional Analysis Paperback - 2006
by Giuseppe Da Prato
From the rear cover
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.
Details
- Title An Introduction to Infinite-Dimensional Analysis
- Author Giuseppe Da Prato
- Binding Paperback
- Edition 1st
- Pages 208
- Volumes 1
- Language ENG
- Publisher Springer
- Date 2006-07-03
- Illustrated Yes
- ISBN 9783540290209 / 3540290206
- Weight 0.78 lbs (0.35 kg)
- Dimensions 9.34 x 6.08 x 0.51 in (23.72 x 15.44 x 1.30 cm)
- Library of Congress Catalog Number 2006924566
- Dewey Decimal Code 530.8
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