On Multidimensional stable-driven Stochastic Differential Equations with Besov drift

Abstract : 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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Contributor : Paul-Eric Chaudru de Raynal <>
Submitted on : Sunday, July 28, 2019 - 2:13:18 PM
Last modification on : Wednesday, July 31, 2019 - 1:15:41 AM

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  • HAL Id : hal-02196382, version 1
  • ARXIV : 1907.12263

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Paul-Eric Chaudru de Raynal, Stéphane Menozzi. On Multidimensional stable-driven Stochastic Differential Equations with Besov drift. 2019. ⟨hal-02196382⟩

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