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. [18], [7]. 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-8,
author = {Ernest Nieznaj},
title = {Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {187-205},
zbl = {1135.60343},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-8}
}
Ernest Nieznaj. Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 187-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-8/