Almost sure behavior for the local time of a diffusion in a spectrally negative Lévy environment

Grégoire Véchambre (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We study the almost sure asymptotic behavior of the supremum of the local time for a transient diffusion in a spectrally negative Lévy environment. In particular, we link this behavior with the left tail of an exponential functional of the environment conditioned to stay positive.

Mots clés: Diffusion; random potential; Lévy process; renewal process; local time; Lévy process conditioned to stay positive; exponential functional

Domaines: Probabilités [math.PR]

Grégoire Véchambre. Almost sure behavior for the local time of a diffusion in a spectrally negative Lévy environment. 2017. ⟨hal-01494335⟩