Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment

Volume 53 / 2005

Ernest Nieznaj 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.

Authors

  • Ernest NieznajDepartment of Mathematics
    Faculty of Electrical Engineering and Computer Science
    Lublin University of Technology
    Nadbystrzycka 38A
    20-618 Lublin, Poland
    e-mail

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