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Regularity of Harmonic Functions for Some Markov Chains with Unbounded Range

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  • Fangjun Xu

    (University of Kansas)

Abstract

We consider a class of continuous time Markov chains on ℤ d . These chains are the discrete space analogue of Markov processes with jumps. Under some conditions, as we show, harmonic functions associated with these Markov chains are Hölder continuous.

Suggested Citation

  • Fangjun Xu, 2013. "Regularity of Harmonic Functions for Some Markov Chains with Unbounded Range," Journal of Theoretical Probability, Springer, vol. 26(2), pages 541-556, June.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:2:d:10.1007_s10959-012-0412-9
    DOI: 10.1007/s10959-012-0412-9
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
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