Generalized functions on infinite dimensional spaces and its applications to white noise calculus (Q1824825)
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scientific article; zbMATH DE number 4118995
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized functions on infinite dimensional spaces and its applications to white noise calculus |
scientific article; zbMATH DE number 4118995 |
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Generalized functions on infinite dimensional spaces and its applications to white noise calculus (English)
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1989
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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.
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generalized function
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abstract Wiener spaces
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white noise
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generalized Brownian functional
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Fourier transform
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composition of a tempered distribution with the Brownian motion
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Itô formula for generalized Brownian functionals
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Kubo-Takenaka theorem for stochastic integration
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