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Transience of symmetric non-local Dirichlet forms (2101.03442v2)
Published 9 Jan 2021 in math.PR
Abstract: We establish transience criteria for symmetric non-local Dirichlet forms on $L2({\mathbb R}d)$ 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.