The Annals of Probability
- Ann. Probab.
- Volume 35, Number 3 (2007), 915-934.
On the continuity of local times of Borel right Markov processes
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.
Ann. Probab., Volume 35, Number 3 (2007), 915-934.
First available in Project Euclid: 10 May 2007
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Eisenbaum, Nathalie; Kaspi, Haya. On the continuity of local times of Borel right Markov processes. Ann. Probab. 35 (2007), no. 3, 915--934. doi:10.1214/009117906000000980. https://projecteuclid.org/euclid.aop/1178804318