Boundary harnack inequality for Markov processes with jumps

Krzysztof Bogdan*, Takashi Kumagai, Mateusz Kwaśnicki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds for positive harmonic functions in arbitrary open sets. It applies, e.g., to many subordinate Brownian motions, Lévy processes with and without continuous part, stable-like and censored stable processes, jump processes on fractals, and rather general Schrödinger, drift and jump perturbations of such processes.

Original languageEnglish
Pages (from-to)477-517
Number of pages41
JournalTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - 2015
Externally publishedYes


  • Boundary harnack inequality
  • Jump Markov process

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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