Weak backward error analysis for SDEs (Q2903058)
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scientific article; zbMATH DE number 6070638
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak backward error analysis for SDEs |
scientific article; zbMATH DE number 6070638 |
Statements
23 August 2012
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Euler-Maruyama method
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Kolmogorov operator
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weak backward error analysis
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invariant measure
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Weak backward error analysis for SDEs (English)
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This paper shows that for the Euler-Maruyama method applied to a stochastic differential equation (SDE), it possesses a modified Kolmogorov operator that can be expanded in powers of the stepsize. In the case the SDE is elliptic or hypoelliptic, a weak backward error analysis result holds. This implies that every invariant measure of the method is close to a modified invariant measure obtained by asymptotic expansion, and that the method is exponentially mixing up to some very small error and for all times.
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