Exit problem of McKean-Vlasov diffusions in convex landscapes

Abstract

The exit time and the exit location of a non-Markovian diffusion is analyzed. More particularly, we focus on the so-called self-stabilizing process. The question has been studied by Herrmann, Imkeller and Peithmann (in 2008) with results similar to those by Freidlin and Wentzell. We aim to provide the same results by a more intuitive approach and without reconstructing the proofs of Freidlin and Wentzell. Our arguments are as follows. In one hand, we establish a strong version of the propagation of chaos which allows to link the exit time of the McKean-Vlasov diffusion and the one of a particle in a mean-field system. In the other hand, we apply the Freidlin-Wentzell theory to the associated mean field system, which is a Markovian diffusion.