Moderate deviations for diffusions in a random Gaussian shear flow drift

We prove quenched and annealed moderate deviation principle in large time for random additive functional of Brownian motion integral(0)(t) v(B-S) ds, where B is a d-dimensional Brownian motion, and v is a stationary Gaussian field from R-d with value in R, independent of the Brownian motion. The speed of the moderate deviations is linked to the decay of correlation of the random field. The results are proved in dimension d less than or equal to 3. These random additive functionals are the central object in the study of diffusion processes with random drift X-t = W-t + integral(0)(t) V(X-S)ds, where V is a centered Gaussian shear flow random field independent of the Brownian W. (C) 2004 Elsevier SAS. All rights reserved.