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Communications in Mathematical Physics

, Volume 266, Issue 3, pp 699–714 | Cite as

Homogenization of Ornstein-Uhlenbeck Process in Random Environment

  • Gaël Benabou
Article

Abstract

We consider a tracer particle moving in a random environment. The velocity of the tracer is modelled by an Ornstein-Uhlenbeck process which takes into account inertia and friction. The medium results in a possibly unbounded random potential. We prove an invariance principle for this kind of motion. The method used is generalized in order to obtain a central limit theorem for a large class of process, the most interesting application being a tagged particle in a medium of infinitely many Ornstein-Uhlenbeck particles.

Keywords

Central Limit Theorem Dirichlet Form Random Environment Invariance Principle Resolvent Equation 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Ceremade, UMR CNRS 7534Université Paris IX - DauphineParis Cedex 16France

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