A remark on subharmonicity for symmetric Dirichlet forms

Abstract

We remove the local boundedness for ${\mathcal{E}}_{\hat{I}}\pm$-subharmonicity in the framework of (not necessarily strongly local) regular symmetric Dirichlet form $(\mathcal{E},D(\mathcal{E}))$ with $\hat{I}\pm \ge 0$ and establish the stochastic characterization for $\mathcal{E}$-subharmonic functions without assuming the local boundedness.