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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 $X$.
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https://hal.archives-ouvertes.fr/hal-01152982
Contributor : Pierre Andreoletti <>
Submitted on : Tuesday, August 30, 2016 - 10:04:09 AM
Last modification on : Monday, February 10, 2020 - 6:13:49 PM

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

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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⟩

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