论文标题
奇异的McKean-Vlasov（反射）SDE具有分布依赖性噪声
Singular McKean-Vlasov (Reflecting) SDEs with Distribution Dependent Noise
论文作者
论文摘要
通过使用Zvonkin的转换和分布中的两个步骤的固定点论点，具有具有分布相关的噪声的单一奇异麦基恩 - 维拉索夫SDE的范围和规律性估计值是在空间和局部分布中线性增长的，并且在空间和噪声中的分布中，在空间和局部分布中，该术语在太空和局部分布中均与空间差异的分布相关，而在空间和lights explies中的分布相关，则在空间和局部分布中线性增长，而在空间和lipschits中的分布相关，则是差异的分布。距离。主要结果扩展了与分布无关的噪声系数的现有结果，或在分布中具有很好的线性功能衍生物。还研究了与分布相关噪声的单数反射SDE。
By using Zvonkin's transformation and a two-step fixed point argument in distributions, the well-posedness and regularity estimates are derived for singular McKean-Vlasov SDEs with distribution dependent noise, where the drift contains a term growing linearly in space and distribution and a locally integrable term independent of distribution, while the noise coefficient is weakly differentiable in space and Lipschitz continuous in distribution with respect to the sum of Wasserstein and weighted variation distances. The main results extend existing ones derived for noise coefficients either independent of distribution, or having nice linear functional derivatives in distribution. Singular reflecting SDEs with distribution dependent noise are also studied.
