论文标题
具有分布漂移和Lévy噪声的多维SDE
Multidimensional SDE with distributional drift and Lévy noise
论文作者
论文摘要
我们通过研究相关的（奇异的）martingale问题并解决kolmogorov向后方程来求解由对称的分布漂移，$α$ - 稳定的莱维流程驱动的分布漂移，并允许在正规$ 3 $（2-2-2α）中，我们可以更好地理解，我们可以很好地理解，我们可以很好地理解''规律性比$（1-α）/2 $。在低规律性方程中，Kolmogorov向后的方程是基于paracontroll的分布。 关键字：奇异扩散，稳定的lévy噪声，分布漂移，副控制分布，BROX扩散
We solve multidimensional SDEs with distributional drift driven by symmetric, $α$-stable Lévy processes for $α\in (1,2]$ by studying the associated (singular) martingale problem and by solving the Kolmogorov backward equation. We allow for drifts of regularity $(2-2α)/3$, and in particular we go beyond the by now well understood "Young regime", where the drift must have better regularity than $(1-α)/2$. The analysis of the Kolmogorov backward equation in the low regularity regime is based on paracontrolled distributions. As an application of our results we construct a Brox diffusion with Lévy noise. Keywords: Singular diffusions, stable Lévy noise, distributional drift, paracontrolled distributions, Brox diffusion
