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.
General
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