On harmonic functions for trace processes

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review


Let X be a standard Markov process with state space E and let F be a closed subset of E. A nonnegative function f on F is extended probabilistically to a function hf on the whole space E. We show that the extension hf is harmonic with respect to X provided that f is harmonic with respect to Y, the trace process on F of the process X. A consequence is that if the Harnack inequality holds for X, it also holds for the trace process Y. Several examples illustrating the usefulness of the result are given.

Original languageEnglish (US)
Pages (from-to)1889-1902
Number of pages14
JournalMathematische Nachrichten
Issue number14-15
StatePublished - Oct 2011


  • Harmonic function
  • Harnack inequality
  • Standard process
  • Trace process

ASJC Scopus subject areas

  • Mathematics(all)


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