On subhamonicity for symmetric Markov processes

2009/12/16 by Zhen-Qing Chen, Chen, Zhen-Qing, Kazuhiro Kuwae +1 · 1 citation
Mathematics · #31C05 #60J25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 60J45 #Probability (math.PR) #Secondary 31C25 #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0912.3290

openalex publication_date 2009/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• A remark on subharmonicity for symmetric Dirichlet forms

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