Backward multivalued McKean-Vlasov SDEs and associated variational inequalities

Abstract

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we establish the well-posedness for multivalued McKean-Vlasov stochastic systems under non-Lipschitz conditions. Then for multiscale multivalued McKean-Vlasov stochastic systems with parameters, in accordance with the values of these parameters we obtain four different average principles. Finally, based on these results, a large deviation principle is presented by a weak convergence approach.