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

TL;DR

This paper proves strong and weak well-posedness of McKean-Vlasov SDEs driven by alpha-stable processes under a unified condition on the kernel's regularity, extending understanding of these stochastic equations.

Contribution

It establishes the strong well-posedness of McKean-Vlasov SDEs driven by alpha-stable processes with a Hölder kernel, under conditions matching the known weak well-posedness threshold.

Findings

Strong well-posedness established for alpha-stable driven McKean-Vlasov SDEs

Unified condition on kernel regularity for both strong and weak well-posedness

Extends previous results to a broader class of stochastic equations

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.