The maximum of the local time of a diffusion process in a drifted Brownian potential

Alexis Devulder (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider a one-dimensional diffusion process in a drifted Brownian potential. We are interested in the maximum of its local time, and study its almost sure asymptotic behaviour, which is proved to be different from the behaviour of the maximum local time of the transient random walk in random environment.

Mots clés: Random environment; diffusion in a random potential; maximum local time; Lévy class

Domaines: Probabilités [math.PR]

Alexis Devulder. The maximum of the local time of a diffusion process in a drifted Brownian potential. 2006. ⟨hal-00022214v1⟩