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Working paper

Well-posedness of some non-linear stable driven SDEs

math. arxive. Cornell University, 2019. No. 1910.05945.
Frikha N., Konakov V., Menozzi S.
We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKeanVlasov driven by non-degenerate symmetric α-stable L´evy processes with values in R^d under some mild Holder 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). New strong well-posedness results are also derived from the previous analysis.