HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# RENEWAL STRUCTURE AND LOCAL TIME FOR DIFFUSIONS IN RANDOM ENVIRONMENT

Abstract : 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 $X$.
Keywords :
Document type :
Journal articles
Domain :
Complete list of metadata

Cited literature [38 references]

https://hal.archives-ouvertes.fr/hal-01152982
Contributor : Pierre Andreoletti Connect in order to contact the contributor
Submitted on : Tuesday, August 30, 2016 - 10:04:09 AM
Last modification on : Monday, December 13, 2021 - 9:16:23 AM

### Files

LocalT_DRE_53_ALEA_AVEC_FIGURE...
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01152982, version 5
• ARXIV : 1506.02895

### Citation

Pierre Andreoletti, Alexis Devulder, Grégoire Vechambre. RENEWAL STRUCTURE AND LOCAL TIME FOR DIFFUSIONS IN RANDOM ENVIRONMENT. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2016. ⟨hal-01152982v5⟩

Record views