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An introduction to infinite-dimensional analysis

✍ Scribed by Giuseppe da Prato

Book ID
127425599
Publisher
Springer
Year
2006
Tongue
English
Weight
1 MB
Series
Universitext
Edition
1
Category
Library
City
Berlin
ISBN
3540290206

No coin nor oath required. For personal study only.

✦ Synopsis

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.Β 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 ofΒ  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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