Approximation of invariant foliations for stochastic dynamical systems (Q2888816)
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scientific article; zbMATH DE number 6042637
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of invariant foliations for stochastic dynamical systems |
scientific article; zbMATH DE number 6042637 |
Statements
4 June 2012
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stable and unstable foliations
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fibre
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asymptotic expansion
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gap condition
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Approximation of invariant foliations for stochastic dynamical systems (English)
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For the abstract stochastic differential equation \(du=\bigl(Au+F(u)\bigr)\,dt+\varepsilon u\circ dW(t)\) on a separable Hilbert space, where \(A\) is linear, generating a \(C^0\) semigroup with an exponential dichotomy, \(F\) is smooth and globally Lipschitz with \(F(0)=0\) and \(DF(0)=0\), and \(W\) is a real-valued standard Wiener process, the stable fibres of the stochastic system and of the deterministic system obtained for \(\varepsilon=0\) are investigated by invoking an expansion in \(\varepsilon\).
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