An Introduction to Infinite-Dimensional Analysis

2006
ISBN: 978-3-642-42168-6
Verlag: Springer

Buch, Englisch, 208 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Da Prato, Giuseppe

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

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.

Über Autor(innen)

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.