Asymptotic analysis for the generalized langevin equation
Mathematical Physics
2015-05-18 v1 math.MP
Abstract
Various qualitative properties of solutions to the generalized Langevin equation (GLE) in a periodic or a confining potential are studied in this paper. We consider a class of quasi-Markovian GLEs, similar to the model that was introduced in \cite{EPR99}. Geometric ergodicity, a homogenization theorem (invariance principle), short time asymptotics and the white noise limit are studied. Our proofs are based on a careful analysis of a hypoelliptic operator which is the generator of an auxiliary Markov process. Systematic use of the recently developed theory of hypocoercivity \cite{Vil04HPI} is made.
Keywords
Cite
@article{arxiv.1003.4203,
title = {Asymptotic analysis for the generalized langevin equation},
author = {M. Ottobre and G. A. Pavliotis},
journal= {arXiv preprint arXiv:1003.4203},
year = {2015}
}
Comments
27 pages, no figures. Submitted to Nonlinearity.