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

TL;DR

This paper studies the asymptotic behaviors of path-dependent multivalued McKean-Vlasov stochastic differential equations under small noise, establishing large deviation, moderate deviation, and central limit theorems.

Contribution

It introduces new methods to analyze the asymptotic behaviors of complex path-dependent McKean-Vlasov equations with non-Lipschitz coefficients.

Findings

Established a large deviation principle for the equations.

Derived a moderate deviation principle using an auxiliary equation.

Proved a central limit theorem for the 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.