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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2502.03712 |
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Table des matières:
- We obtain the unique weak and strong solvability for time inhomogeneous stochastic differential equations with the drift in subcritical Lebesgue--Hölder spaces $L^p([0,T];{\mathcal C}_b^β({\mathbb R}^d;{\mathbb R}^d))$ and driven by $α$-stable processes for $α\in (0,2)$. The weak well-posedness is derived for $β\in (0,1)$, $α+β>1$ and $p>α/(α+β-1)$ through Prohorov's theorem, Skorohod's representation and the regularity estimates of solutions for a class of fractional parabolic partial differential equations. The pathwise uniqueness and Davie's type uniqueness are proved for $β>1-α/2$ by using Itô--Tanaka's trick. Moreover, we give a counterexample to the pathwise uniqueness for the supercritical Lebesgue--Hölder drifts to explain the present result is sharp.