In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.
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Ma, Z., Zhu, R. & Zhu, X. On notions of harmonicity for non-symmetric Dirichlet form. Sci. China Math. 53, 1407–1420 (2010). https://doi.org/10.1007/s11425-010-4001-z
- harmonic functions
- uniformly integrable martingale
- SPV integrable
- non-symmetric Dirichlet forms
- non-symmetric Beurling-Deny decomposition
- Hunt processes