Transience of symmetric nonlocal Dirichlet forms

Yuichi Shiozawa

Mathematische Nachrichten, 2023, vol. 296, issue 5, 2121-2149

Abstract: We establish transience criteria for symmetric nonlocal Dirichlet forms on L2(Rd;dx)$L^2({\mathbb {R}}^d;{\rm d}x)$ 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.

Date: 2023
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https://doi.org/10.1002/mana.202100052

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