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

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  • Gabriel Faraud

    (Université Paris 13 CNRS, UMR 7539 LAGA 99)

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.

Suggested Citation

  • Gabriel Faraud, 2011. "Estimates on the Speedup and Slowdown for a Diffusion in a Drifted Brownian Potential," Journal of Theoretical Probability, Springer, vol. 24(1), pages 194-239, March.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:1:d:10.1007_s10959-009-0251-5
    DOI: 10.1007/s10959-009-0251-5
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    Cited by:

    1. Grégoire Véchambre, 2023. "Almost Sure Behavior for the Local Time of a Diffusion in a Spectrally Negative Lévy Environment," Journal of Theoretical Probability, Springer, vol. 36(2), pages 876-925, June.

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