Journal of Statistical Physics

, Volume 117, Issue 1–2, pp 261–279 | Cite as

Periodic Homogenization for Hypoelliptic Diffusions

  • M. Hairer
  • G. A. Pavliotis
Article

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 in several metrics.

periodic homogenization hypoellipticity martingale central limit theorem convergence rate Wasserstein metric 

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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • M. Hairer
    • 1
  • G. A. Pavliotis
    • 1
  1. 1.Mathematics InstituteThe University of WarwickUnited Kingdom

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