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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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.

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

First available in Project Euclid: 8 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Permanental processes Markov processes local times


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.

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