Estimates on the speedup and slowdown for a diffusion in a drifted brownian potential

Details Estimates on the speedup and slowdown for a diffusion in a drifted brownian potential Estimates on the speedup and slowdown for a diffusion in a drifted brownian potential

2009-07-10

arxiv.org/abs/0907.1864v2

Journal of theoretical Probability, 2011, Volume 24, Number 1, Pages 194-239

Mathematics

Probability

Scientific paper

10.1007/s10959-009-0251-5

We study a model of diffusion in a brownian potential. This model was firstly introduced by T. Brox (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 (1997), and a decomposition of hitting times developed in a recent article by A. Fribergh, N. Gantert and S. Popov (2008). Our results are in agreement with their results in the discrete case.

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