The Annals of Probability

Moderate deviations for diffusions with Brownian potentials

Yueyun Hu and Zhan Shi

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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.

Article information

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

Dates
First available in Project Euclid: 8 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1107883351

Digital Object Identifier
doi:10.1214/009117904000000829

Mathematical Reviews number (MathSciNet)
MR2094443

Zentralblatt MATH identifier
1066.60096

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

Keywords
Moderate deviation diffusion with random potential Brownian valley

Citation

Hu, Yueyun; Shi, Zhan. Moderate deviations for diffusions with Brownian potentials. Ann. Probab. 32 (2004), no. 4, 3191--3220. doi:10.1214/009117904000000829. https://projecteuclid.org/euclid.aop/1107883351


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References

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