Journal of the Mathematical Society of Japan

On subharmonicity for symmetric Markov processes

Zhen-Qing CHEN and Kazuhiro KUWAE

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Abstract

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

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

Dates
First available in Project Euclid: 29 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1351516773

Digital Object Identifier
doi:10.2969/jmsj/06441181

Mathematical Reviews number (MathSciNet)
MR2998921

Zentralblatt MATH identifier
1263.60073

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1351516773


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