The Annals of Probability

Moderate deviations for diffusions with Brownian potentials

Yueyun Hu and Zhan Shi

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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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Ann. Probab., Volume 32, Number 4 (2004), 3191-3220.

First available in Project Euclid: 8 February 2005

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments 60F10: Large deviations

Moderate deviation diffusion with random potential Brownian valley


Hu, Yueyun; Shi, Zhan. Moderate deviations for diffusions with Brownian potentials. Ann. Probab. 32 (2004), no. 4, 3191--3220. doi:10.1214/009117904000000829.

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