Gaussian distributions and applications to stochastic partial differential equations (Q2712775)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gaussian distributions and applications to stochastic partial differential equations |
scientific article |
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2 December 2001
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Gaussian distribution
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white noise analysis
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Fock space
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partial differential equation
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Gaussian distributions and applications to stochastic partial differential equations (English)
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The paper is devoted to the problems of white noise analysis. Let \(B\) be a complex Banach space. The author considers the projective limit \(\varepsilon_k (N')\) of the spaces of holomorphic functions \(f:B\rightarrow \mathbb{C}\). Also, he introduces chaotic transformation, or \(S\)-transform, that plays in the theory of infinite-dimensional partial differential equations the same role as Fourier transformation in the finite-dimensional case. Four theorems about the properties of \(\varepsilon_k (N')\) and \(S\)-transform are formulated. They are generalized to the case of \(\varepsilon_{\theta}(N')\) where \(\theta\) is an increasing convex function (Young function). Applications to heat equation and stochastic Wick-type Burgers equation are presented.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00063].
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