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Periodic Homogenization for Hypoelliptic Diffusions

M. Hairer·G. A. Pavliotis
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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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M. Hairer, G. A. Pavliotis. 2004-03-03. Periodic Homogenization for Hypoelliptic Diffusions. https://doi.org/10.1023/b%3Ajoss.0000044055.59822.20

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