Abstract
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.
Original language | English |
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Pages (from-to) | 1407-1420 |
Number of pages | 14 |
Journal | Science China Mathematics |
Volume | 53 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2010 |
Externally published | Yes |
Keywords
- Harmonic functions
- Hunt processes
- Non-symmetric Beurling-Deny decomposition
- Non-symmetric Dirichlet forms
- SPV integrable
- Uniformly integrable martingale
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Ma, Z. M., Zhu, R. C., & Zhu, X. C. (2010). On notions of harmonicity for non-symmetric Dirichlet form. Science China Mathematics, 53(6), 1407-1420. https://doi.org/10.1007/s11425-010-4001-z