On Multidimensional stable-driven Stochastic Differential Equations with Besov drift
Résumé
We establish well-posedness results for multidimensional non degenerate α-stable driven SDEs with time inhomogeneous singular drifts in L^r-B^{−1+γ}_{p,q} with γ < 1 and α in (1, 2], where L^r and B^{−1+γ}_{p,q} stand for Lebesgue and Besov spaces respectively. Precisely, we first prove the well-posedness of the corresponding martingale problem and then give a precise meaning to the dynamics of the SDE. Our results rely on the smoothing properties of the underlying PDE, which is investigated by combining a perturbative approach with duality results between Besov spaces.
Domaines
Probabilités [math.PR]| Origine | Fichiers produits par l'(les) auteur(s) |
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