论文标题
对称稳定过程的常规子空间
Regular subspaces of symmetric stable processes
论文作者
论文摘要
粗略地说，常规子空间是常规的dirichlet表单，它们以较小的域继承了原始形式。在本文中，考虑了1-DIM对称$α$稳定过程的常规子空间。主要的结果是，当且仅当$α\ [1,2] $中的$α\时，它可以接收适当的常规子空间。此外，对于$α\ in（1,2）$，给出了常规子空间的表征。一般的1-DIM对称莱维过程也将进行研究。可以证明，它是否具有适当的常规子空间与其样品路径是否具有有限变化密切相关。
Roughly speaking, regular subspaces are regular Dirichlet forms that inherit the original forms with smaller domains. In this paper, regular subspaces of 1-dim symmetric $α$-stable processes are considered. The main result is that it admits proper regular subspaces if and only if $α\in [1,2]$. Moreover, for $α\in(1,2)$, the characterization of the regular subspaces is given. General 1-dim symmetric Lévy processes will also be investigated. It will be shown that whether it has proper regular subspaces is closely related to whether its sample paths have finite variation.
