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Moderate deviations for diffusions with Brownian potentials. (English) Zbl 1066.60096

Summary: 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 F. Comets and S. Popov [Probab. Theory Relat. Fields 126, 571–609 (2003; Zbl 1027.60091] who studied the corresponding problem for Sinai’s random walk in random environment.

MSC:

60K37 Processes in random environments
60F10 Large deviations

Citations:

Zbl 1027.60091
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References:

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