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]. Some results similar to the ones of Freidlin and Wentzell for classical diffusions have been proved. We aim to provide the same results by a method more intuitive. Our arguments are the uniform propagation of chaos and the application of the Freidlin-Wentzell theory to a mean-field system. Moreover, we provide a new kind of uniform propagation of chaos in the small noise.

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. 2011. ⟨hal-00628262v1⟩