论文标题
非线性差异问题的杀死分布依赖的SDE
Killed Distribution Dependent SDE for Nonlinear Dirichlet Problem
论文作者
论文摘要
为了表征开放型域中的非线性差异问题，我们调查了杀死的分布依赖性SDE。通过投影构建耦合并使用Zvonkin/girsanov变换，在三种不同的情况下证明了拟态的性能：1）单调性盒具有分布相关的噪声（可能是变性），2）奇异案例，2）具有非分布依赖性噪声的奇异病例，并且3）具有非分量分布分布独立噪声的奇异案例。在前两种情况下，域是$ c^2 $平滑的，因此也得出了初始分布中Lipschitz的连续性，在最后的情况下，域是任意的。
To characterize nonlinear Dirichlet problems in an open domain, we investigate killed distribution dependent SDEs. By constructing the coupling by projection and using the Zvonkin/Girsanov transforms, the well-posedness is proved for three different situations: 1) monotone case with distribution dependent noise (possibly degenerate), 2) singular case with non-degenerate distribution dependent noise, and 3) singular case with non-degenerate distribution independent noise. In the first two cases the domain is $C^2$ smooth such that the Lipschitz continuity in initial distributions is also derived, and in the last case the domain is arbitrary.
