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Explosion of Jump-Type Symmetric Dirichlet Forms on ℝ d

Author

Listed:
  • Yuichi Shiozawa

    (Okayama University)

  • Toshihiro Uemura

    (Kansai University)

Abstract

We give a sufficient condition for a class of jump-type symmetric Dirichlet forms on ℝ d to be conservative in terms of the jump kernel and the associated measure. Our condition allows the coefficients dominating big jumps to be unbounded. We derive the conservativeness for Dirichlet forms related to symmetric stable processes. We also show that our criterion is sharp by using time changed Dirichlet forms. We finally remark that our approach is applicable to jump-diffusion type symmetric Dirichlet forms on ℝ d .

Suggested Citation

  • Yuichi Shiozawa & Toshihiro Uemura, 2014. "Explosion of Jump-Type Symmetric Dirichlet Forms on ℝ d," Journal of Theoretical Probability, Springer, vol. 27(2), pages 404-432, June.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:2:d:10.1007_s10959-012-0424-5
    DOI: 10.1007/s10959-012-0424-5
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    References listed on IDEAS

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    1. 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.
    2. T. Uemura, 2004. "On Symmetric Stable-Like Processes: Some Path Properties and Generators," Journal of Theoretical Probability, Springer, vol. 17(3), pages 541-555, July.
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