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.
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Hairer, M., Pavliotis, G.A. Periodic Homogenization for Hypoelliptic Diffusions. Journal of Statistical Physics 117, 261–279 (2004). https://doi.org/10.1023/B:JOSS.0000044055.59822.20
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DOI: https://doi.org/10.1023/B:JOSS.0000044055.59822.20