Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 187-205
MSC: Primary 60K37; Secondary 82D30.
DOI: 10.4064/ba53-2-8
Abstract
We prove the central limit theorem for symmetric diffusion processes with non-zero drift in a random environment. The case of zero drift has been investigated in e.g. \cite{varadhan}, \cite{kozlov1}. In addition we show that the covariance matrix of the limiting Gaussian random vector corresponding to the diffusion with drift converges, as the drift vanishes, to the covariance of the homogenized diffusion with zero drift.
