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

Gabriel Faraud (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Diffusion in a random potential; Random walks in random environment; Stochastic calculus; Moderate deviations; Brownian motion

Domaines: Probabilités [math.PR]

Gabriel Faraud. Estimates on the speedup and slowdown for a diffusion in a drifted brownian potential. Journal of Theoretical Probability, 2011, 24 (1), pp.194-239. ⟨10.1007/s10959-009-0251-5⟩. ⟨hal-00600242⟩