Asymptotic behaviors of multiscale multivalued stochastic systems with small noises

Abstract: In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with small noises in the slow components, we prove the strong convergence in the functional law of large numbers by the time discretization scheme. Then for those systems whose slow diffusion coefficients don't depend on the fast components, the large deviation principle is established by the weak convergence approach.