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Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2021

WELL-POSEDNESS OF SOME NON-LINEAR STABLE DRIVEN SDES

Abstract

We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate symmetric $α$-stable Lévy processes with values in $R^d$ 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 $\alpha \in (0, 1)$. New strong well-posedness results are also derived from the previous analysis.
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Dates and versions

hal-02314239 , version 1 (11-10-2019)

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Noufel Frikha, Valentin Konakov, Stéphane Menozzi. WELL-POSEDNESS OF SOME NON-LINEAR STABLE DRIVEN SDES. Discrete and Continuous Dynamical Systems - Series A, 2021, 41 (2), pp.849-898. ⟨10.3934/dcds.2020302⟩. ⟨hal-02314239⟩
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