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BIT Numerical Mathematics

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01.12.2015

Weak backward error analysis for Langevin process

verfasst von: Marie Kopec

Erschienen in: BIT Numerical Mathematics | Ausgabe 4/2015

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Abstract

We consider numerical approximations of stochastic Langevin equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamics associated with the considered implicit scheme is exponentially mixing: The law of the scheme converges exponentially fast to a constant up to an error that we can optimize.

Vorheriger Artikel The multivariate Horner scheme revisited

Nächster Artikel An efficient collocation method for a Caputo two-point boundary value problem

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Titel: Weak backward error analysis for Langevin process
verfasst von: Marie Kopec
Publikationsdatum: 01.12.2015
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 4/2015
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-015-0546-0

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