Self-interacting diffusions: long-time behaviour and exit-problem in the convex case

Ashot Aleksian; Pierre del Moral; Aline Kurtzmann; Julian Tugaut

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arXiv · 2303.14997

Self-interacting diffusions: long-time behaviour and exit-problem in the convex case

Ashot Aleksian·Pierre del Moral·Aline Kurtzmann·Julian Tugaut

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Abstract

We study a class of time-inhomogeneous diffusion: the self-interacting one. We show a convergence result with a rate of convergence that does not depend on the diffusion coefficient. Finally, we establish a so-called Kramers' type law for the first exit-time of the process from domain of attractions when the landscapes are uniformly convex.

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Ashot Aleksian, Pierre del Moral, Aline Kurtzmann, Julian Tugaut. 2023-03-27. Self-interacting diffusions: long-time behaviour and exit-problem in the convex case. https://arxiv.org/abs/2303.14997

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