04-58 M. Hairer, G. A. Pavliotis

Periodic Homogenization for Hypoelliptic Diffusions (171K, PDF) Mar 3, 04

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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.

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