Harnack Inequality for Subordinate Random Walks

Ante Mimica and Stjepan Šebek ()
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Ante Mimica: University of Zagreb
Stjepan Šebek: University of Zagreb

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 737-764

Abstract: 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.

Keywords: Random walk; Subordination; Harnack inequality; Harmonic function; Green function; Poisson kernel; Primary: 60J45; Secondary: 60G50; 60J10; 05C81 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0821-5

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