RENEWAL STRUCTURE AND LOCAL TIME FOR DIFFUSIONS IN RANDOM ENVIRONMENT
Résumé
We study a one-dimensional diffusion $X$ in a drifted Brownian potential $W_\kappa$, with $ 0<\kappa<1$, and focus on the behavior of the local times $(\mathcal{L}(t,x),x)$ of $X$ before time $t>0$.
In particular we characterize the limit law of the supremum of the local time, as well as the position of the favorite sites. These limits can be written explicitly from a two dimensional stable Lévy process. Our analysis is based on the study of an extension of the renewal structure which is deeply involved in the asymptotic behavior of $X$.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)