Small noise asymptotic behaviors for path-dependent multivalued McKean-Vlasov stochastic differential equations

Abstract: This paper investigates the asymptotic behavior of path-dependent multivalued McKean-Vlasov stochastic differential equations perturbed by small noise. Specifically, we first establish a large deviation principle for such equations under non-Lipschitz coefficients by the weak convergence approach. Subsequently, we introduce an auxiliary equation and apply it to derive the moderate deviation principle. Finally, we construct another auxiliary equation and a limit equation, and prove the central limit theorem.