An Introduction to Analysis on Wiener Space

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This text gives the basis of the probabilistic functional analysis on Wiener space, developed since the 1980s. The subject has progressed considerably through its links with QFT and the impact of Stochastic Calculus of Variations of P. Malliavin. Although the latter deals essentially with the regularity of the laws of random variables defined on the Wiener space, the book focuses on quite different subjects, such as independence, Ramer’s theorem, and so forth. First year graduate level in functional analysis and theory of stochastic processes is required (stochastic integration with respect to Brownian motion, Ito formula, etc.). It can be taught as a 1-semester course as it is, or in 2 semesters adding preliminaries from the theory of stochastic processes.