On the continuity of local times of Borel right Markov processes

• 成果类型: Article
• 署名作者: Eisenbaum, Nathalie; Kaspi, Haya
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000980
• 发表日期: 2007
• 页码: 915-934
• 关键词: gaussian-processes; Levy processes; THEOREM

摘要

The problem of finding a necessary and sufficient condition for the continuity of the local times for a general Markov process is still open. Barlow and Hawkes have completely treated the case of the Levy processes, and Marcus and Rosen have solved the case of the strongly symmetric Markov processes. We treat here the continuity of the local times of Borel right processes. Our approach unifies that of Barlow and Hawkes and of Marcus and Rosen, by using an associated Gaussian process, that appears as a limit in a CLT involving the local time process.