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An Introduction to Infinite-Dimensional Analysis 2006 Edition
Contributor(s): Da Prato, Giuseppe (Author)

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 ISBN: 3540290206     ISBN-13: 9783540290209
Publisher: Springer
OUR PRICE: $52.24  

Binding Type: Paperback - See All Available Formats & Editions
Published: July 2006
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Annotation:

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.

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Additional Information
BISAC Categories:
- Mathematics | Mathematical Analysis
- Mathematics | Differential Equations - General
- Mathematics | Probability & Statistics - General
Dewey: 530.8
LCCN: 2006924566
Series: Universitext
Physical Information: 0.51" H x 6.08" W x 9.34" L (0.78 lbs) 208 pages
Features: Bibliography, Illustrated, Index, Table of Contents
 
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Publisher Description:

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts 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 basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
 
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