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Central limit theorem for diffusion processes in an anisotropic random environment. (English) Zbl 1135.60343

The paper concerns with the proof of the central limit theorem for symmetric diffusion processes with non zero drift in random environment. The case with zero drift was studied in [G. C. Papanicolaou, S. R. S. Varadhan, Boundary value problems with rapidly oscillating random coefficients. Random fields, Vol. I, II. Random fields. Rigorous results in statistical mechanics and quantum field theory, Esztergom 1979, Colloq. Math. Soc. Janos Bolyai 27, 835–873 (1981; Zbl 0499.60059)] and [S. M. Kozlov, Mat. Sb., N. Ser. 109(151), 188–202 (1979; Zbl 0415.60059), English translation: Math. USSR, Sb. 37, 167–180 (1980; Zbl 0444.60047)]. Furthermore the author proves the continuity of the covariance matrix with respect to the drift.

MSC:

60K37 Processes in random environments
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
60F05 Central limit and other weak theorems
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