Well-posedness of some non-linear stable driven SDEs

Abstract

<p style='text-indent:20px;'>We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric <inline-formula><tex-math id="M1">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>-stable Lévy processes with values in <inline-formula><tex-math id="M2">\begin{document}$ {{{\mathbb R}}}^d $\end{document}</tex-math></inline-formula> under some mild Hölder regularity assumptions on the drift and diffusion coefficients with respect to both space and measure variables. The methodology developed here allows to consider unbounded drift terms even in the so-called super-critical case, i.e. when the stability index <inline-formula><tex-math id="M3">\begin{document}$ \alpha \in (0,1) $\end{document}</tex-math></inline-formula>. New strong well-posedness results are also derived from the previous analysis.