Deviation estimates for multivalued McKean-Vlasov stochastic differential equations

TL;DR

This paper establishes deviation estimates, including large, moderate, and central limit theorems, for multivalued McKean-Vlasov stochastic differential equations using weak convergence and $L$-derivatives.

Contribution

It introduces deviation principles for multivalued McKean-Vlasov SDEs, combining large deviation, central limit, and moderate deviation results with novel analytical methods.

Findings

Proved large deviation principle via weak convergence.

Established central limit theorem using $L$-derivatives.

Derived moderate deviation principle for the equations.

Abstract

The work concerns deviation estimates for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the large deviation principle for them by the weak convergence approach. Then the central limit theorem for them is shown with the help of a formula for $L$-derivatives. Finally, we establish the moderate deviation principle for them.