We make the split of integral fractional Laplacian as $(-\Delta)^s u=(-\Delta)(-\Delta)^{s-1}u$, where $s\in(0,\frac{1}{2})\cup(\frac{1}{2},1)$. Based on this splitting, we respectively discretize one- and two-dimensional with inhomogeneous Dirichlet boundary condition give corresponding truncation errors help interpolation estimate. Moreover, suitable corrections are proposed to guarantee conv...

To characterize nonlinear Dirichlet problems in an open domain, we investigate killed distribution dependent SDEs. By constructing the coupling by projection and using Zvonkin/Girsanov transforms, well-posedness is proved for three different situations:1) monotone case with noise (possibly degenerate);2) singular non-degenerate noise;3) independent noise. In first two cases domain $ C^2 smooth ...