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

Details A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes and loop soups A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes and loop soups

2010-05-31

arxiv.org/abs/1005.5692v1

Mathematics

Probability

Scientific paper

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 the local times. We show that for certain Markov processes the associated permanental process is equal in distribution to the loop soup local time.

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