The Annals of Probability

A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes

Michael B. Marcus and Jay Rosen

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Abstract

We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for continuity which is also known to be necessary. Using an isomorphism theorem of Eisenbaum and Kaspi which relates Markov local times and permanental processes, we obtain a general sufficient condition for the joint continuity of local times.

Article information

Source
Ann. Probab., Volume 41, Number 2 (2013), 671-698.

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1362750938

Digital Object Identifier
doi:10.1214/12-AOP744

Mathematical Reviews number (MathSciNet)
MR3077522

Zentralblatt MATH identifier
1329.60273

Subjects
Primary: 60K99: None of the above, but in this section 60J55: Local time and additive functionals
Secondary: 60G17: Sample path properties

Keywords
Permanental processes Markov processes local times

Citation

Marcus, Michael B.; Rosen, Jay. A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes. Ann. Probab. 41 (2013), no. 2, 671--698. doi:10.1214/12-AOP744. https://projecteuclid.org/euclid.aop/1362750938


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References

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