Periodic Homogenization for Hypoelliptic Diffusions

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.

References in corpus (3)

• Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
• Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators
• Periodic Homogenization for Inertial Particles

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