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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2015

Weak backward error analysis for overdamped Langevin processes

Résumé

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.

Dates et versions

hal-00905684 , version 1 (18-11-2013)

Identifiants

Citer

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