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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.