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Large deviations for a Poisson random indexed branching process

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  • Gao, Zhenlong
  • Wang, Weigang

Abstract

Consider a Galton–Watson process {Zn} and an independent Poisson process {Nt}, the continuous time process {ZNt} is a Poisson random indexed branching process. We show the large deviation results for P(ZNt≤ect) and P(ZNt≥ect).

Suggested Citation

  • Gao, Zhenlong & Wang, Weigang, 2015. "Large deviations for a Poisson random indexed branching process," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 143-148.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:143-148
    DOI: 10.1016/j.spl.2015.06.013
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    References listed on IDEAS

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    1. Gao, Zhenlong & Zhang, Yanhua, 2015. "Large and moderate deviations for a class of renewal random indexed branching process," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 1-5.
    2. Mitov, Georgi K. & Mitov, Kosto V. & Yanev, Nikolay M., 2009. "Critical randomly indexed branching processes," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1512-1521, July.
    3. Huang, Chunmao & Liu, Quansheng, 2012. "Moments, moderate and large deviations for a branching process in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 522-545.
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    Cited by:

    1. Gao, Zhenlong & Wang, Weigang, 2016. "Large and moderate deviations for a renewal randomly indexed branching process," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 139-145.

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