Science China Mathematics

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

On notions of harmonicity for non-symmetric Dirichlet form

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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.

Keywords

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

MSC(2000)

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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