Moderate deviations for diffusions with Brownian potentials
نویسندگان
چکیده
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 [3] who studied the corresponding problem for Sinai’s random walk in random environment.
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