Large deviations from the mckean-vlasov limit for weakly interacting diffusions

Abstract

A system of N diffusions on R$SUP:D$ESUP:in which the interaction is expressed in terms of the empirical measure is considered. The limiting behavior as N →∞ is described by a McKean_Vlasov equation. The purpose of this paper is to show that the large deviations from the McKean-Vlasov limit can be described by a generalization of the theory of Freidlin and Wentzell and to obtain a characterization of the action functional. In order to obtain this action functional we first obtain results on projective limits of large deviation systems, large deviations on dual vector spaces and a Sanov type theorem for vectors of empirical measures