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Theses

Sur certains processus aléatoires en milieu aléatoire

Abstract : This thesis's aim is to study random processes in a random environment. This kind of processes was introduced for the first time in 1965 by A.A. Chernov, and has received much attention since. Besides the elementary unidimensional model studied by A.A. Chernov, numerous attempts have been made in order to apply a similar approach to different contexts. We focus in particular on two examples. First we study the case of random walk in a random environment on trees, for which we extend a recurrence/transience criterion due to R. Lyons and R. Pemantle, before studying the asymptotic behavior in the critical case. In a first case we give a central limit theorem, while in a second one we show that the walk behave like (logn)3. In the intermediate regime between those two behaviors, we refer to previous work by Y. Hu and Z. Shi. In a second part we study a time continuous process in a random environment, known as Brox's diffusion. We extend to this context some recent results due to A. Fribergh, N. Gantert and S. Popov about speedup and slowdown.
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Submitted on : Wednesday, February 16, 2011 - 2:02:50 PM
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  • HAL Id : tel-00566478, version 1

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Gabriel Faraud. Sur certains processus aléatoires en milieu aléatoire. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2010. Français. ⟨tel-00566478⟩

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