Science China Mathematics

, Volume 53, Issue 6, pp 1407–1420 | Cite as

On notions of harmonicity for non-symmetric Dirichlet form

  • ZhiMing Ma
  • RongChan Zhu
  • XiangChan Zhu


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.


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


30P12 32C12 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesPeking UniversityBeijingChina

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