We establish the equivalence of the analytic and probabilistic notions of subharmonicity in the framework of general symmetric Hunt processes on locally compact separable metric spaces, extending an earlier work of the first named author on the equivalence of the analytic and probabilistic notions of harmonicity. As a corollary, we prove a strong maximum principle for locally bounded finely continuous subharmonic functions in the space of functions locally in the domain of the Dirichlet form under some natural conditions.
"On subharmonicity for symmetric Markov processes." J. Math. Soc. Japan 64 (4) 1181 - 1209, October, 2012. https://doi.org/10.2969/jmsj/06441181