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Zbl 1042.60009
Castell, Fabienne
Moderate deviations for diffusions in a random Gaussian shear flow drift. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 3, 337-366 (2004). ISSN 0246-0203

Summary: We prove quenched and annealed moderate deviation principle in large time for random additive functional of Brownian motion $\int_0^t v(B_s) ds$, where $B$ is a $d$-dimensional Brownian motion, and $v$ is a stationary Gaussian field from $\Bbb R^d$ with value in $\Bbb R$, independent of the Brown\-ian motion. The speed of the moderate deviations is linked to the decay of correlation of the random field. The results are proved in dimension $d \leqslant 3$. These random additive functionals are the central object in the study of diffusion processes with random drift $X_t=W_t+\int_0^t V(X_s) ds$, where $V$ is a centered Gaussian shear flow random field independent of the Brownian $W$.

MSC 2000:: *60F10 Large deviations
60J55 Additive functionals
60K37 Processes in random environments

Keywords: Large and moderate deviations; Additive functionals of Brownian motion; Random media; Anderson model

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