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Berry–Esseen bound for a supercritical branching processes with immigration in a random environment

Author

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  • Huang, Xulan
  • Li, Yingqiu
  • Xiang, Kainan

Abstract

Let (Zn) be a supercritical branching process with immigration (Yn) in an independent and identically distributed environment ξ. We consider the rate of convergence of the normalized population Wn=Zn/Πn to its limit W, where (Πn) is the usually used norming sequence, and establish a Berry–Esseen bound. Similar results are also obtained for Wn+k−Wn for each fixed positive integer k.

Suggested Citation

  • Huang, Xulan & Li, Yingqiu & Xiang, Kainan, 2022. "Berry–Esseen bound for a supercritical branching processes with immigration in a random environment," Statistics & Probability Letters, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:stapro:v:190:y:2022:i:c:s0167715222001535
    DOI: 10.1016/j.spl.2022.109619
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    References listed on IDEAS

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    1. Yingqiu Li & Xulan Huang, 2022. "A.s. convergence rate for a supercritical branching processes with immigration in a random environment," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(3), pages 826-839, February.
    2. Wang, Hesong & Gao, Zhiqiang & Liu, Quansheng, 2011. "Central limit theorems for a supercritical branching process in a random environment," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 539-547, May.
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