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

Ashot Aleksian; Julian Tugaut

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arXiv · 2310.20471

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

Ashot Aleksian·Julian Tugaut

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Abstract

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.

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BibTeX RIS

Ashot Aleksian, Julian Tugaut. 2023-10-31. Measure-dependent non-linear diffusions with superlinear drifts: asymptotic behaviour of the first exit-times. https://arxiv.org/abs/2310.20471

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