A Class of Singular Symmetric Markov Processes

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• 作者：Fangjun Xu (1)
  
• 关键词：Dirichlet form ; Lévy process ; Stable process ; Nash inequality ; Harmonic function ; Support theorem ; H?lder continuity ; Primary 60J75 ; Secondary 31B05 ; 60J35
• 刊名：Potential Analysis
• 出版年：2013
• 出版时间：January 2013
• 年：2013
• 卷：38
• 期：1
• 页码：207-232
• 参考文献：1. Bass, R.F.: Diffusions and Elliptic Operators. Springer, New York (1997)
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• 作者单位：Fangjun Xu (1)
  
  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045-7594, USA
  
• ISSN：1572-929X

文摘

We consider a class of pure jump Markov processes in ${\mathbb R}^d$ whose jump kernels are comparable to that of a certain d-dimensional Lévy process. Upper and lower bounds for the transition densities of these processes are obtained. We show that bounded harmonic functions associated with these processes are H?lder continuous.