Exit problem of McKean-Vlasov diffusions in convex landscape

Julian Tugaut (1)

1 Universität Bielefeld = Bielefeld University

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 [Herrmann, Imkeller, Peithmann|2008]. They proved some results similar to the ones of Freidlin and Wentzell. We aim to provide the same results by an approach more intuitive 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 permits 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.

Mots clés: Self-stabilizing diffusion; Exit time; Exit location; Large deviations; Interacting particle systems; Propagation of chaos; Granular media equation

Domaines: Probabilités [math.PR]

Julian Tugaut. Exit problem of McKean-Vlasov diffusions in convex landscape. 2012. ⟨hal-00628262v2⟩