Hairer, MartinPavliotis, G. A.2024-09-172024-09-172024-09-112004-10-0110.1023/B:JOSS.0000044055.59822.202-s2.0-5444253857https://infoscience.epfl.ch/handle/20.500.14299/241185We 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.enfalseconvergence ratehypoellipticitymartingale central limit theoremperiodic homogenizationWasserstein metrictext::journal::journal article::research article