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Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates

Author

Listed:
  • Zhen-Qing Chen

    (University of Washington)

  • Yan-Xia Ren

    (Peking University)

  • Ting Yang

    (Beijing Institute of Technology
    Beijing Key Laboratory on MCAACI)

Abstract

We establish weak and strong laws of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the branching mechanism being general and state dependent. Our work is motivated by recent work on the strong law of large numbers for branching symmetric Markov processes by Chen and Shiozawa (J Funct Anal 250:374–399, 2007) and for branching diffusions by Engländer et al. (Ann Inst Henri Poincaré Probab Stat 46:279–298, 2010). Our results can be applied to some interesting examples that are covered by neither of these papers.

Suggested Citation

  • Zhen-Qing Chen & Yan-Xia Ren & Ting Yang, 2017. "Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates," Journal of Theoretical Probability, Springer, vol. 30(3), pages 898-931, September.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:3:d:10.1007_s10959-016-0671-y
    DOI: 10.1007/s10959-016-0671-y
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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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