CLT and MDP for McKean-Vlasov SDEs

TL;DR

This paper extends the classical CLT and moderate deviation principles to McKean-Vlasov SDEs, which are stochastic differential equations with distribution-dependent coefficients, under Lipschitz conditions.

Contribution

It establishes the CLT and moderate deviation principles specifically for McKean-Vlasov SDEs, broadening the theoretical understanding from classical to distribution-dependent cases.

Findings

CLT and moderate deviation principles are proven for McKean-Vlasov SDEs.

Results extend classical SDE results to distribution-dependent settings.

Provides theoretical foundation for analyzing fluctuations in McKean-Vlasov SDEs.

Abstract

Under a Lipschitz condition on distribution dependent coefficients, the central limit theorem and the moderate deviation principle are obtained for solutions of McKean-Vlasov type stochastic differential equations, which extend from the corresponding results for classical stochastic differential equations to the distribution dependent setting.