Well-posedness and propagation of chaos for Lévy-driven McKean-Vlasov SDEs under Lipschitz assumptions
Résumé
The first goal of this note is to prove the strong well-posedness of McKean-Vlasov SDEs driven by Lévy 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 a particular mean-field system of interacting stable-driven Ornstein-Uhlenbeck processes.
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