On subharmonicity for symmetric Markov processes. (English) Zbl 1263.60073

The equivalence of the analytic and probabilistic definitions for subharmonicity is established in the framework of general symmetric Hunt processes on locally compact separable metric spaces. This extends a similar result (for harmonicity), obtained by Z.-Q. Chen [Proc. Am. Math. Soc. 137, No. 10, 3497–3510 (2009; Zbl 1181.60118)]. As a corollary, a strong maximum principle is proved for locally bounded finely continuous subharmonic functions in the space of functions which are locally in the domain of the Dirichlet form.


60J45 Probabilistic potential theory
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
31C25 Dirichlet forms
60J25 Continuous-time Markov processes on general state spaces


Zbl 1181.60118
Full Text: DOI arXiv Euclid


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