Journal of the Mathematical Society of Japan

On subharmonicity for symmetric Markov processes

Zhen-Qing CHEN and Kazuhiro KUWAE

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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.

Article information

J. Math. Soc. Japan, Volume 64, Number 4 (2012), 1181-1209.

First available in Project Euclid: 29 October 2012

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Zentralblatt MATH identifier

Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 31C05: Harmonic, subharmonic, superharmonic functions
Secondary: 31C25: Dirichlet spaces 60J25: Continuous-time Markov processes on general state spaces

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


CHEN, Zhen-Qing; KUWAE, Kazuhiro. On subharmonicity for symmetric Markov processes. J. Math. Soc. Japan 64 (2012), no. 4, 1181--1209. doi:10.2969/jmsj/06441181.

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