Measure-dependent non-linear diffusions with superlinear drifts: asymptotic behaviour of the first exit-times

Autor:	Aleksian, Ashot, Tugaut, Julian
Rok vydání:	2023
Předmět:	Mathematics - Probability Primary: 60H10 Secondary: 60J60 60K35
Druh dokumentu:	Working Paper
Popis:	In this paper, we study McKean-Vlasov SDE living in $\mathbb{R}^d$ in the reversible case without assuming any type of convexity assumptions for confinement or interaction potentials. Kramers' type law for the exit-time from a domain of attraction is established. Namely, in the small-noise regime, the limit in probability of the first exit-time behaves exponentially. This result is established using the large deviations principle as well as improved coupling method. Having removed the convexity assumption, this work is a major improvement of the previously known results for the exit-time problem, the review of which is provided in the paper. Comment: 36 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.20471 Zobrazit plný text záznamu View this record from Arxiv