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On notions of harmonicity for non-symmetric Dirichlet form

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.

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Correspondence to RongChan Zhu.

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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

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Keywords

  • harmonic functions
  • uniformly integrable martingale
  • SPV integrable
  • non-symmetric Dirichlet forms
  • non-symmetric Beurling-Deny decomposition
  • Hunt processes

MSC(2000)

  • 30P12
  • 32C12