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Transience of symmetric nonlocal Dirichlet forms

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  • Yuichi Shiozawa

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.

Suggested Citation

  • Yuichi Shiozawa, 2023. "Transience of symmetric nonlocal Dirichlet forms," Mathematische Nachrichten, Wiley Blackwell, vol. 296(5), pages 2121-2149, May.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:5:p:2121-2149
    DOI: 10.1002/mana.202100052
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    References listed on IDEAS

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    1. Haruna Okamura & Toshihiro Uemura, 2021. "On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities," Journal of Theoretical Probability, Springer, vol. 34(2), pages 809-826, June.
    2. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
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