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

2023/10/31 by Ashot Aleksian, Julian Tugaut, Aleksian, Ashot +1
Economics, Econometrics and Finance · Mathematics · #60K35 #FOS: Mathematics #Mathematical Biology Tumor Growth #Primary: 60H10 #Probability (math.PR) #Secondary: 60J60 #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2310.20471

openalex publication_date 2023/10/31 · openalex created_date 2023/11/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we study McKean-Vlasov SDE living in 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.

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