An introduction to infinite-dimensional analysis
著者
書誌事項
An introduction to infinite-dimensional analysis
（Universitext）
Springer, c2006
- : pbk
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注記
Includes bibliographical references (p. [207]-208) and index
内容説明・目次
内容説明
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.
目次
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.
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