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.
"A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes." Ann. Probab. 41 (2) 671 - 698, March 2013. https://doi.org/10.1214/12-AOP744