Transience of symmetric nonlocal Dirichlet forms

Abstract

AbstractWe establish transience criteria for symmetric nonlocal Dirichlet forms on in terms of the coefficient growth rates at infinity. Applying these criteria, we find a necessary and sufficient condition for recurrence of Dirichlet forms of symmetric stable‐like with unbounded/degenerate coefficients. This condition indicates that both of the coefficient growth rates of small and big jump parts affect the sample path properties of the associated symmetric jump processes.