Harnack inequalities and difference estimates for random walks with infinite range
The authors study difference estimates and Harnack inequalities for aperiodic, mean zero finite variance random walks in \(\mathbb{Z}^ d\) with infinite range. An example is given showing that such estimates and inequalities do not necessarily hold for mean zero, finite variance random walks. Conditions on the transition function \(p\) of the walk are given ensuring that appropriate forms of difference estimates and Harnack-type inequalities hold. As a corollary, usual difference estimates and Harnack inequalities are obtained for aperiodic, mean zero, finite variance random walks with finite range.
scientific article; zbMATH DE number 563114