The Annals of Probability

On the continuity of local times of Borel right Markov processes

Nathalie Eisenbaum and Haya Kaspi

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Abstract

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.

Article information

Source
Ann. Probab., Volume 35, Number 3 (2007), 915-934.

Dates
First available in Project Euclid: 10 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1178804318

Digital Object Identifier
doi:10.1214/009117906000000980

Mathematical Reviews number (MathSciNet)
MR2319711

Zentralblatt MATH identifier
1126.60066

Subjects
Primary: 60F05: Central limit and other weak theorems 60G15: Gaussian processes 60J25: Continuous-time Markov processes on general state spaces 60J55: Local time and additive functionals

Keywords
Markov processes local time central limit theorem Gaussian processes

Citation

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


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References

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