Infinite dimensional stochastic equation with multiplicative noise in spaces of stochastic distributions (Q2853218)
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scientific article; zbMATH DE number 6217171
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infinite dimensional stochastic equation with multiplicative noise in spaces of stochastic distributions |
scientific article; zbMATH DE number 6217171 |
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18 October 2013
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Cauchy problem
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white noise
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Hermite transform
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Infinite dimensional stochastic equation with multiplicative noise in spaces of stochastic distributions (English)
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The authors investigate existence of a strong solution of a stochastic differential equation involving multiplicative noise. Solutions are found in the spaces of Hilbert space-valued generalized stochastic functionals (separable Hilbert space-valued Kondratiev distributions). After applying the Hermite transform, the stochastic differential equation reduces to a deterministic equation which can be solved by classical \(C_0\)-semigroup theory.
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