An Introduction to Infinite-Dimensional Analysis

Giuseppe Da Prato

ISBN 10: 3540290206 / ISBN 13: 9783540290209

Editore: Springer Berlin Heidelberg, 2006

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783540290209

Dati bibliografici

• Titolo: An Introduction to Infinite-Dimensional Analysis
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 3540290206
• ISBN 13: 9783540290209
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

GIUSEPPE DA PRATO was born in La Spezia in 1936. Having graduated in Physics in 1960 from the University of Rome, he became full professor of Mathematics in 1968 and taught in Rome and in Trento. Since 1979 he has been Professor of Mathematical Analysis at the Scuola Normale Superiore di Pisa.

The scientific activity of Giuseppe Da Prato concerns infinite-dimensional analysis and partial differential stochastic equations (existence, uniqueness, invariant measures, ergodicity), with applications to optimal stochastic control.

Giuseppe Da Prato is the author of 5 other books, some co-authored with other international specialists, on control theory, stochastic differential equations and infinite dimensional Kolmogorov equations, and of more than 250 papers in international scientific journals.