Central limit theorem and moderate deviation principle for McKean-Vlasov SDEs (Q2051411)

The authors investigate the central limit theorem and the moderate deviation principle for solutions of McKean-Vlasov SDEs using the weak convergence approach. More precisely, the authors first show that the law of the solution to a good approximation SDE of the underlying McKean-Vlasov SDEs satisfies an large deviation principle via weak convergence method. It is worth noting that the weak convergence approach results in a convenient representation formula for the rate function. Secondly, the authors show that the solution to an approximation SDE and the solution to the McKean-Vlasov SDEs are exponentially equivalent as the deviation scale tends to zero.