HAL : hal-00321069, version 4

arXiv : 0809.2195

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v1 (12-09-2008)

v2 (11-09-2009)

v3 (31-05-2010)

v4 (15-09-2010)

Limit law of the local time for Brox's diffusion

Pierre Andreoletti 1, Roland Diel 1

(02/07/2009)

We consider Brox's model: a one-dimensional diffusion in a Brownian potential W. We show that the normalized local time process (L(t;m_(log t) + x)=t; x \in R), where m_(log t) is the bottom of the deepest valley reached by the process before time t, behaves asymptotically like a process which only depends on W. As a consequence, we get the weak convergence of the local time to a functional of two independent three-dimensional Bessel processes and thus the limit law of the supremum of the normalized local time. These results are discussed and compared to the discrete time and space case which same questions have been solved recently by N. Gantert, Y. Peres and Z. Shi.

1 :	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349

Domaine

:

Mathématiques/Probabilités

Mots Clés : Diffusion process in random environment – local time

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Contributeur : Roland Diel <>

Soumis le : Lundi 13 Septembre 2010, 11:29:16

Dernière modification le : Mercredi 15 Septembre 2010, 10:03:16