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Weak backward error analysis for overdamped Langevin processes

Marie Kopec 1, 2, *
* Corresponding author
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We consider numerical approximations of overdamped Langevin stochastic differential 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 dynamic associated with the implicit scheme considered is exponentially mixing.
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Submitted on : Monday, November 18, 2013 - 3:30:38 PM
Last modification on : Thursday, January 7, 2021 - 4:36:05 PM

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Marie Kopec. Weak backward error analysis for overdamped Langevin processes. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2015, 35 (2), pp.583-614. ⟨10.1093/imanum/dru016⟩. ⟨hal-00905684⟩



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