Moderate deviations for diffusions with Brownian potentials

Details Moderate deviations for diffusions with Brownian potentials Moderate deviations for diffusions with Brownian potentials

2005-03-25

arxiv.org/abs/math/0503591v1

Annals of Probability 2004, Vol. 32, No. 4, 3191-3220

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000829 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000829

We present precise moderate deviation probabilities, in both quenched and annealed settings, for a recurrent diffusion process with a Brownian potential. Our method relies on fine tools in stochastic calculus, including Kotani's lemma and Lamperti's representation for exponential functionals. In particular, our result for quenched moderate deviations is in agreement with a recent theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003) 571-609] who studied the corresponding problem for Sinai's random walk in random environment.

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