Well-posedness and propagation of chaos for L{\'e}vy-driven McKean-Vlasov SDEs under Lipschitz assumptions

Abstract

The first goal of this note is to prove the strong well-posedness of McKean-Vlasov SDEs driven by L{\'e}vy processes on $\mathbb{R}^d$ having a finite moment of order $\beta \in [1,2]$ and under standard Lipschitz assumptions on the coefficients. Then, we prove a quantitative propagation of chaos result at the level of paths for the associated interacting particle system, with constant diffusion coefficient. Finally, we improve the rates of convergence obtained for linear interactions with respect to the measure and when the noise is a $\alpha$-stable process with $\alpha \in (1,2)$, for which we have $\beta < \alpha$.