Open Access
October, 2012 On subharmonicity for symmetric Markov processes
Zhen-Qing CHEN, Kazuhiro KUWAE
J. Math. Soc. Japan 64(4): 1181-1209 (October, 2012). DOI: 10.2969/jmsj/06441181


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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Zhen-Qing CHEN. Kazuhiro KUWAE. "On subharmonicity for symmetric Markov processes." J. Math. Soc. Japan 64 (4) 1181 - 1209, October, 2012.


Published: October, 2012
First available in Project Euclid: 29 October 2012

zbMATH: 1263.60073
MathSciNet: MR2998921
Digital Object Identifier: 10.2969/jmsj/06441181

Primary: 31C05 , 60J45
Secondary: 31C25 , 60J25

Keywords: Dirichlet form , Lévy system , strong maximum principle , subharmonic function , symmetric Hunt process , uniformly integrable submartingale

Rights: Copyright © 2012 Mathematical Society of Japan

Vol.64 • No. 4 • October, 2012
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