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Law of large numbers for supercritical superprocesses with non-local branching

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  • Palau, Sandra
  • Yang, Ting

Abstract

In this paper we establish a weak and a strong law of large numbers for supercritical superprocesses with general non-local branching mechanisms. Our results complement earlier results obtained for superprocesses with only local branching. Several interesting examples are developed, including multitype continuous-state branching processes, multitype superdiffusions and superprocesses with discontinuous spatial motions and non-decomposable branching mechanisms.

Suggested Citation

  • Palau, Sandra & Yang, Ting, 2020. "Law of large numbers for supercritical superprocesses with non-local branching," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1074-1102.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:1074-1102
    DOI: 10.1016/j.spa.2019.04.007
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    References listed on IDEAS

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    1. Kyprianou, Andreas E. & Palau, Sandra, 2018. "Extinction properties of multi-type continuous-state branching processes," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3466-3489.
    2. Kouritzin, Michael A. & Ren, Yan-Xia, 2014. "A strong law of large numbers for super-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 505-521.
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    Cited by:

    1. Yan-Xia Ren & Ting Yang, 2024. "Limiting Distributions for a Class of Super-Brownian Motions with Spatially Dependent Branching Mechanisms," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2457-2507, September.

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