Multidimensional SDE with distributional drift and Lévy noise

@article{Kremp2020MultidimensionalSW,
  title={Multidimensional SDE with distributional drift and L{\'e}vy noise},
  author={Helena Kremp and Nicolas Perkowski},
  journal={arXiv: Probability},
  year={2020}
}
We solve multidimensional SDEs with distributional drift driven by symmetric, $\alpha$-stable Levy processes for $\alpha\in (1,2]$ by studying the associated (singular) martingale problem and by solving the Kolmogorov backward equation. We allow for drifts of regularity $(2-2\alpha)/3$, and in particular we go beyond the by now well understood "Young regime", where the drift must have better regularity than $(1-\alpha)/2$. The analysis of the Kolmogorov backward equation in the low regularity… 
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