Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts

Abstract

We study reflected McKean–Vlasov diffusions over a convex, non-bounded domain with self-stabilising coefficients that do not satisfy the classical Wasserstein Lipschitz condition. We establish existence and uniqueness results for this class and address the propagation of chaos. Our results are of wider interest, without the McKean–Vlasov component they extend reflected SDE theory, and without the reflective term they extend the McKean–Vlasov theory. We prove a Freidlin–Wentzell type Large Deviations Principle and an Eyring–Kramer’s law for the exit-time from subdomains contained in the interior of the reflecting domain. Our characterisation of the rate function for the exit-time distribution is explicit.

Daniel Adams

Maths and Stats Developer

My research interests include Wasserstein gradient flows, large deviations, interacting particle systems, non-equilibrium dynamics and homogenization.