On the exit-problem for self-interacting diffusions V2 - Inria - Institut national de recherche en sciences et technologies du numérique
Preprints, Working Papers, ... Year : 2022

On the exit-problem for self-interacting diffusions V2

Abstract

We study the exit-time from a domain of a self-interacting diffusion, where the Brownian motion is replaced by $\sigma B_t$ for a constant $\sigma$. The first part of this work consists in showing that the rate of convergence (of the occupation measure of the self-interacting process toward some explicit Gibbs measure) previously obtained in \cite{kk-ejp} for a convex confinment potential $V$ and a convex interaction potential can be bounded uniformly with respect to $\sigma$. Then, we prove an Arrhenius-type law for the first exit-time from a domain (satisfying classical hypotheses of Freidlin-Wentzell theory).

Dates and versions

hal-03850314 , version 1 (13-11-2022)

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Ashot Aleksian, Pierre del Moral, Aline Kurtzmann, Julian Tugaut. On the exit-problem for self-interacting diffusions V2. 2022. ⟨hal-03850314⟩
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