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

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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.

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Acknowledgments

The research of Zhen-Qing Chen is partially supported by NSF Grant DMS-1206276 and NNSFC 11128101. The research of Yan-Xia Ren is supported by NNSFC (Grant Nos. 11271030 and 11128101). The research of Ting Yang is partially supported by NNSF of China (Grant No. 11501029) and Beijing Institute of Technology Research Fund Program for Young Scholars.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen

  2. LMAM School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, 100871, People’s Republic of China

    Yan-Xia Ren

  3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Ting Yang

  4. Beijing Key Laboratory on MCAACI, Beijing, 100081, People’s Republic of China

    Ting Yang

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  1. Zhen-Qing Chen
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  2. Yan-Xia Ren
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  3. Ting Yang
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Correspondence to Ting Yang.

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Chen, ZQ., Ren, YX. & Yang, T. Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates. J Theor Probab 30, 898–931 (2017). https://doi.org/10.1007/s10959-016-0671-y

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  • DOI: https://doi.org/10.1007/s10959-016-0671-y

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