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Regular version of the site

Article

Well-Posedness of Some Non-Linear Stable Driven SDEs

Discrete and Continuous Dynamical Systems. 2021. Vol. 41. No. 2. P. 849-898.
Frikha N., Konakov V., Menozzi S.

We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric αα-stable Lévy processes with values in RdRd 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 α∈(0,1)α∈(0,1). New strong well-posedness results are also derived from the previous analysis.