On notions of harmonicity for non-symmetric Dirichlet form

Zhi Ming Ma; Rong Chan Zhu; Xiang Chan Zhu

doi:10.1007/s11425-010-4001-z

On notions of harmonicity for non-symmetric Dirichlet form

Zhi Ming Ma, Rong Chan Zhu, Xiang Chan Zhu

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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
Pages (from-to)	1407-1420
Number of pages	14
Journal	Science China Mathematics
Volume	53
Issue number	6
DOIs	https://doi.org/10.1007/s11425-010-4001-z
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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10.1007/s11425-010-4001-z

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KW - Non-symmetric Beurling-Deny decomposition

KW - Non-symmetric Dirichlet forms

KW - SPV integrable

KW - Uniformly integrable martingale

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On notions of harmonicity for non-symmetric Dirichlet form

Abstract

Keywords

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