arXiv Open Access 2022

On the exit-problem for self-interacting diffusions

Ashot Aleksian Pierre Del Moral Aline Kurtzmann Julian Tugaut

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Abstrak

We study the exit-time from a domain of a self-interacting diffusion, where the Brownian motion is replaced by $σB_t$ for a constant $σ$. 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 $σ$. Then, we prove an Arrhenius-type law for the first exit-time from a domain (satisfying classical hypotheses of Freidlin-Wentzell theory).

Topik & Kata Kunci

math.PR

Penulis (4)

Ashot Aleksian

Pierre Del Moral

Aline Kurtzmann

Julian Tugaut

Format Sitasi

APA MLA BibTeX

Aleksian, A., Moral, P.D., Kurtzmann, A., Tugaut, J. (2022). On the exit-problem for self-interacting diffusions. https://arxiv.org/abs/2201.10428

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓