Small noise asymptotics of multi-scale McKean-Vlasov stochastic dynamical systems

Abstract

The main aim of this work is to investigate small noise limiting behavior of multi-scale McKean-Vlasov stochastic dynamical systems, where we allow the coefficients depend on the distributions of both slow and fast components. Firstly, the strong convergence in the functional law of large numbers is established by the time discretization scheme. Secondly, in order to characterize the probability of deviations away from the averaged limit, we prove the large deviation principle by the weak convergence approach for McKean-Vlasov equations.