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Harnack Inequality for Subordinate Random Walks

Author

Listed:
  • Ante Mimica

    (University of Zagreb)

  • Stjepan Šebek

    (University of Zagreb)

Abstract

In this paper, we consider a large class of subordinate random walks X on the integer lattice $$\mathbb {Z}^d$$ Z d via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero. We establish estimates for one-step transition probabilities, the Green function and the Green function of a ball, and prove the Harnack inequality for nonnegative harmonic functions.

Suggested Citation

  • Ante Mimica & Stjepan Šebek, 2019. "Harnack Inequality for Subordinate Random Walks," Journal of Theoretical Probability, Springer, vol. 32(2), pages 737-764, June.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:2:d:10.1007_s10959-018-0821-5
    DOI: 10.1007/s10959-018-0821-5
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    References listed on IDEAS

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    1. Kim, Panki & Song, Renming & Vondraček, Zoran, 2014. "Global uniform boundary Harnack principle with explicit decay rate and its application," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 235-267.
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