Weak backward error analysis for Langevin process
Numerical Analysis
2013-10-11 v1 Probability
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.
Cite
@article{arxiv.1310.2599,
title = {Weak backward error analysis for Langevin process},
author = {Marie Kopec},
journal= {arXiv preprint arXiv:1310.2599},
year = {2013}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1105.0489 by other authors; and substantial text overlap with arXiv:1310.2404