Harnack Inequality for Subordinate Random Walks

In this paper, we consider a large class of subordinate random walks X on the integer lattice \(\mathbb {Z}^d\) 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.