Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment

Ernest Nieznaj¹

¹ Department of Mathematics Faculty of Electrical Engineering and Computer Science Lublin University of Technology Nadbystrzycka 38A 20-618 Lublin, Poland

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 2, pp. 187-205.

Résumé

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.

Détail

DOI : 10.4064/ba53-2-8

Keywords: prove central limit theorem symmetric diffusion processes non zero drift random environment zero drift has investigated cite varadhan cite kozlov addition covariance matrix limiting gaussian random vector corresponding diffusion drift converges drift vanishes covariance homogenized diffusion zero drift