On the continuity of local times of Borel right Markov processes

Details On the continuity of local times of Borel right Markov processes On the continuity of local times of Borel right Markov processes

2005-12-27

arxiv.org/abs/math/0512599v2

Annals of Probability 2007, Vol. 35, No. 3, 915-934

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000980 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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 L\'{e}vy 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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