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October 2004 Moderate deviations for diffusions with Brownian potentials
Yueyun Hu, Zhan Shi
Ann. Probab. 32(4): 3191-3220 (October 2004). DOI: 10.1214/009117904000000829

Abstract

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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Yueyun Hu. Zhan Shi. "Moderate deviations for diffusions with Brownian potentials." Ann. Probab. 32 (4) 3191 - 3220, October 2004. https://doi.org/10.1214/009117904000000829

Information

Published: October 2004
First available in Project Euclid: 8 February 2005

zbMATH: 1066.60096
MathSciNet: MR2094443
Digital Object Identifier: 10.1214/009117904000000829

Subjects:
Primary: 60F10, 60K37

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 4 • October 2004
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