On Some Path Properties of Symmetric Stable-Like Processes for One Dimension
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- 作者：Toshihiro Uemura
- 关键词：symmetric stable ; like processes ; exceptionality of points ; recurrence
- 刊名：Potential Analysis
- 出版时间：2002
- 出版年：2002
- 期刊代码：105_09262601
- 类别：bio
- 卷：16
- 期：1
- 页码：79-91
- 数据来源：sp
摘要
We show that a symmetric stable-type form becomes a Dirichlet form in the wide sense under a quite mild assumption and give a necessary and sufficiently condition that the domain contains the family of all uniformly Lipschitz continuous functions with compact support. Moreover we give some path properties of the corresponding Markov processes (we call the processes symmetric stable-like processes) in one dimension such as exceptionality of points and recurrence of the processes. We then note that the recurrence of the processes depend on the behavior of the index functions at the infinity.