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Subcritical superprocesses conditioned on non-extinction

Author

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  • Liu, Rongli
  • Ren, Yan-Xia
  • Song, Renming
  • Sun, Zhenyao

Abstract

We consider a class of subcritical superprocesses (Xt)t≥0 with general spatial motions and general branching mechanisms. We study the asymptotic behaviors of Qt,r, the distribution of Xt conditioned on Xt+r not being a null measure. We first give the existence of limt→∞Qt,r and limr→∞Qt,r, and then show that an LlogL-type condition is equivalent to the existence of the iterated limits: limr→∞limt→∞Qt,r and limt→∞limr→∞Qt,r. Finally, when the LlogL-type condition holds, we show that those iterated limits, and the double limit limr,t→∞Qt,r, are the same.

Suggested Citation

  • Liu, Rongli & Ren, Yan-Xia & Song, Renming & Sun, Zhenyao, 2023. "Subcritical superprocesses conditioned on non-extinction," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 498-534.
    • Handle: RePEc:eee:spapps:v:163:y:2023:i:c:p:498-534
    DOI: 10.1016/j.spa.2023.06.008
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    References listed on IDEAS

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    1. Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2015. "Central limit theorems for supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 428-457.
    2. Liu, Rongli & Ren, Yan-Xia & Song, Renming & Sun, Zhenyao, 2021. "Quasi-stationary distributions for subcritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 108-134.
    3. Ren, Yan-Xia & Song, Renming & Sun, Zhenyao, 2020. "Limit theorems for a class of critical superprocesses with stable branching," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4358-4391.
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