On subhamonicity for symmetric Markov processes

Details On subhamonicity for symmetric Markov processes On subhamonicity for symmetric Markov processes

2009-12-16

arxiv.org/abs/0912.3290v1

Mathematics

Probability

Scientific paper

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.

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