论文标题
概括到dirichlet to-neumann运营商
Generalizing Dirichlet-to-Neumann operators
论文作者
论文摘要
本文的目的是在Dirichlet形式的背景下研究Dirichlet到Neumann的操作员，尤其是找出其概率对应物。关于不可证明的dirichlet形式，我们将证明他们的dirichlet to-neumann运算符与与边界上的时间更改过程相对应的跟踪dirichlet形式相关联。此外，还将探索Dirichlet到Neumann的操作员，以探索Dirichlet形式的扰动。事实证明，对于典型的情况，此类dirichlet to-neumann运算符对应于准直阳性保存（对称）强制性形式，因此存在通过DOOB的$ h $转换与其相关的马尔可夫流程系列。
The aim of this paper is to study the Dirichlet-to-Neumann operators in the context of Dirichlet forms and especially to figure out their probabilistic counterparts. Regarding irreducible Dirichlet forms, we will show that the Dirichlet-to-Neumann operators for them are associated with the trace Dirichlet forms corresponding to the time changed processes on the boundary. Furthermore, the Dirichlet-to-Neumann operators for perturbations of Dirichlet forms will be also explored. It turns out that for typical cases such a Dirichlet-to-Neumann operator corresponds to a quasi-regular positivity preserving (symmetric) coercive form, so that there exists a family of Markov processes associated with it via Doob's $h$-transformations.
