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Generalized functions on infinite dimensional spaces and its applications to white noise calculus. (English) Zbl 0683.46035

The author extends the generalized function theory to abstract Wiener spaces and shows that it provides a suitable framework for the white noise calculus initiated by T. Hida. The notion of a generalized Brownian functional is introduced and the Fourier transform is extended to infinite dimensions. A new definition of the composition of a tempered distribution with the Brownian motion is given. The results obtained are used in verification of the Itô formula for generalized Brownian functionals and the Kubo-Takenaka theorem for stochastic integration.
Reviewer: L.Janos

MSC:

46F25 Distributions on infinite-dimensional spaces
60H05 Stochastic integrals
60J65 Brownian motion
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