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

Chen, Zhen-Qing; Kuwae, Kazuhiro

J. Math. Soc. Japan 64, No. 4, 1181-1209 (2012).

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.

Reviewer: Liliana Popa (Iaşi)

MSC:

60J45	Probabilistic potential theory
31C05	Harmonic, subharmonic, superharmonic functions on other spaces
31C25	Dirichlet forms
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

Citations:

Zbl 1181.60118

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