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

TL;DR

This paper establishes a sufficient condition for the continuity of permanental processes, especially those derived from Gaussian processes, and applies this to ensure joint continuity of Markov local times.

Contribution

It provides a new sufficient condition for the continuity of permanental processes and extends this to local times of Markov processes using an isomorphism theorem.

Findings

Sufficient condition for the continuity of permanental processes.

Necessary and sufficient condition for Gaussian-derived permanental processes.

General sufficient condition for the joint continuity of Markov local times.

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.