论文标题
具有分布相互作用内核的多维稳定驱动的McKean-Vlasov SDE-噪声透视的正则化
Multidimensional Stable driven McKean-Vlasov SDEs with distributional interaction kernel -- a regularization by noise perspective
论文作者
论文摘要
我们有兴趣在Lebesgue-Besov空间的框架中，在具有添加剂稳定的噪声和具有奇异相互作用内核的卷积类型的非线性漂移的McKean-Vlasov SDE和强度较强的稳定性中。特别是，我们定量地表征了非线性允许如何超越具有单数相互作用内核的线性SDE获得的阈值。我们证明，可以实现从噪声缩放的阈值中得出的阈值，并且可以从经典的意义上理解相应的SDE。我们还特别表征当弱和强唯一性之间的二分法时，驱动噪声的稳定性指数的功能以及漂移的参数。
We are interested in establishing weak and strong well-posedness for McKean-Vlasov SDEs with additive stable noise and a convolution type non-linear drift with singular interaction kernel in the framework of Lebesgue-Besov spaces. In particular, we characterize quantitatively how the non-linearity allows to go beyond the thresholds obtained for linear SDEs with singular interaction kernels. We prove that the thresholds deriving from the scaling of the noise can be achieved and that the corresponding SDE can be understood in the classical sense. We also specifically characterize in function of the stability index of the driving noise and the parameters of the drift when the dichotomy between weak and strong uniqueness occurs.
