Convergence in monge-wasserstein distance of mean field systems with locally lipschitz coefficients

Abstract

This paper focuses on stochastic systems of weakly interacting particles whose dynamics depend on the empirical measures of the whole populations. The drift and diffusion coefficients of the dynamical systems are assumed to be locally Lipschitz continuous and satisfy global linear growth condition. The limits of such systems as the number of particles tends to infinity are studied, and the rate of convergence of the sequences of empirical measures to their limits in terms of P ͭ ͪ Monge-Wasserstein distance is established. We also investigate the existence, uniqueness, and boundedness, and continuity of solutions of the limiting McKean-Vlasov equations associated to the systems.