By using the heat kernel parameter expansion with respect to the frozen SDEs, the intrinsic derivative is estimated for the law of Mckean-Vlasov SDEs with respect to the initial distribution. As an application, the total variation distance between the laws of two solutions is bounded by the Wasserstein distance for initial distributions. These extend some recent results proved for distribution-free noise by using the coupling method and Malliavin calculus.
Supported in part by the National Key R&D Program of China (No. 2020YFA0712900) and NNSFC (11771326, 11831014, 11801406, 11921001).
We are grateful to the editors and referees.
"Derivative estimates on distributions of McKean-Vlasov SDEs." Electron. J. Probab. 26 1 - 12, 2021. https://doi.org/10.1214/21-EJP582