Periodic Homogenization for Hypoelliptic Diffusions
Mathematical Physics
2009-11-10 v1 math.MP
Abstract
We study the long time behavior of an Ornstein-Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian motion whose covariance can be expressed in terms of the solution of a Poisson equation. We also derive upper bounds on the convergence rate.
Cite
@article{arxiv.math-ph/0403003,
title = {Periodic Homogenization for Hypoelliptic Diffusions},
author = {M. Hairer and G. A. Pavliotis},
journal= {arXiv preprint arXiv:math-ph/0403003},
year = {2009}
}