Work

Weak backward error analysis for Langevin process

Year: 2013

Type: preprint

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 dynamic associated with the implicit scheme considered is exponentially mixing.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1310.2599

Author: Kopec, Marie

Institutions: École Normale Supérieure Paris-Saclay, Institut national de recherche en sciences et technologies du numérique, École Normale Supérieure de Rennes

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2951044337

Cites: 14

Cited by: 5

Related to: 20