In this paper, we treat a priori estimates of harmonic functions for jump processes associated with non-local operators. Let L be a non-local operator given by Under some conditions on n(x,h), we prove the Hölder continuity and the uniform continuity of L-harmonic functions. Our results are extensions of those obtained by Bass and Kassmann (Commun Part Diff Eq 30:1249-1259, 2005).
- A priori estimates
- Continuity of harmonic functions
- Markov jump processes
- Martingale problem
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