Estimates on the Speedup and Slowdown for a Diffusion in a Drifted Brownian Potential

Gabriel Faraud ()
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Gabriel Faraud: Université Paris 13 CNRS, UMR 7539 LAGA 99

Journal of Theoretical Probability, 2011, vol. 24, issue 1, 194-239

Abstract: Abstract We study a model of diffusion in a Brownian potential. This model was first introduced by T. Brox (Ann. Probab. 14:1206–1218, 1986) as a continuous time analogue of random walk in random environment. We estimate the deviations of this process above or under its typical behavior. Our results rely on different tools such as a representation introduced by Y. Hu, Z. Shi and M. Yor, Kotani’s lemma, introduced at first by K. Kawazu and H. Tanaka (J. Math. Soc. Jpn. 49:189–211, 1997), and a decomposition of hitting times developed in a recent article by A. Fribergh, N. Gantert and S. Popov (Preprint, 2008). Our results are in agreement with their results in the discrete case.

Keywords: Diffusion in a random potential; Random walks in random environment; Stochastic calculus; Moderate deviations; Brownian motion; 60F10; 60K37 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-009-0251-5

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