On asymptotic properties of infinite dimensional stochastic systems. (Q2711583)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On asymptotic properties of infinite dimensional stochastic systems. |
scientific article |
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1999
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stochastic heat equations
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stochastic evolution equations
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Hilbert space
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Wiener process
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spin models
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Burgers equations
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On asymptotic properties of infinite dimensional stochastic systems. (English)
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This paper is devoted to the study stochastic evolution equations of the form NEWLINE\[NEWLINE\begin{cases} dX= (AX+ F(X))\,dt+ B(X)\,dW(t),\\ X(0)= x\in E\end{cases}\tag{1}NEWLINE\]NEWLINE on a Hilbert space \(E\), where \(W(t)\) denotes a Wiener process. The author presents several methods for studying the asymptotic behaviour of (1) and applies them to spin models and to stochastic heat and Burgers equations.
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