Well-Posedness for McKean-Vlasov SDEs with Distribution Dependent Stable Noises

Abstract

The well-posedness is established for McKean-Vlasov SDEs driven by $\alpha$-stable noises ($1<\alpha<2$). In this model, the drift is H\"{o}lder continuous in space variable and Lipschitz continuous in distribution variable with respect to the sum of Wasserstein and weighted variation distances, while the noise coefficient satisfies the Lipschitz condition in distribution variable with respect to the sum of two Wasserstein distances. The main tool relies on Zvonkin's transform, a time-change technique and a two-step fixed point argument.