Asymptotic analysis for the generalized langevin equation

Abstract

Various qualitative properties of solutions to the generalized Langevin equation (GLE) in a periodic or a confining potential are studied in this paper. We consider a class of quasi-Markovian GLEs, similar to the model that was introduced in \cite{EPR99}. Geometric ergodicity, a homogenization theorem (invariance principle), short time asymptotics and the white noise limit are studied. Our proofs are based on a careful analysis of a hypoelliptic operator which is the generator of an auxiliary Markov process. Systematic use of the recently developed theory of hypocoercivity \cite{Vil04HPI} is made.

27 pages, no figures. Submitted to Nonlinearity.

References in corpus (3)

• Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics
• Periodic Homogenization for Hypoelliptic Diffusions
• From ballistic to diffusive behavior in periodic potentials

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