Open Access
May 2007 On the continuity of local times of Borel right Markov processes
Nathalie Eisenbaum, Haya Kaspi
Ann. Probab. 35(3): 915-934 (May 2007). DOI: 10.1214/009117906000000980


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 Lévy 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.


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Nathalie Eisenbaum. Haya Kaspi. "On the continuity of local times of Borel right Markov processes." Ann. Probab. 35 (3) 915 - 934, May 2007.


Published: May 2007
First available in Project Euclid: 10 May 2007

zbMATH: 1126.60066
MathSciNet: MR2319711
Digital Object Identifier: 10.1214/009117906000000980

Primary: 60F05 , 60G15 , 60J25 , 60J55

Keywords: central limit theorem , Gaussian processes , Local time , Markov processes

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • May 2007
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