Strong and weak well-posedness of McKean-Vlasov SDEs driven by $\alpha$-stable processes under unified condition

Abstract

In this paper, we consider $\alpha \in (0,2)$ and establish the strong well-posedness of McKean--Vlasov SDEs driven by an $\alpha$-stable process with a H\"older (Besov) kernel $K \in \mathbf{C}^\beta$, where $\beta > 1-\alpha$. This condition coincides with the well-known threshold for the weak well-posedness.