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Pré-Publication, Document De Travail Année : 2020

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.
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Dates et versions

hal-02196382 , version 1 (28-07-2019)
hal-02196382 , version 2 (01-12-2020)
hal-02196382 , version 3 (14-02-2022)

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Paul-Eric Chaudru de Raynal, Stéphane Menozzi. On Multidimensional stable-driven Stochastic Differential Equations with Besov drift. 2020. ⟨hal-02196382v2⟩
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