Harnack inequality for subordinate random walks

2017/01/26 by Mimica, Ante, Šebek, Stjepan
#60J45 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1701.07690

Abstract

In this paper, we consider a large class of subordinate random walks X on integer lattice ℤ^d via subordinators with Laplace exponents which are complete Bernstein functions satisfying a certain lower scaling condition 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 non-negative harmonic functions.

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