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Central limit theorems for a supercritical branching process in a random environment

Author

Listed:
  • Wang, Hesong
  • Gao, Zhiqiang
  • Liu, Quansheng

Abstract

For a supercritical branching process (Zn) in a stationary and ergodic environment [xi], we study the rate of convergence of the normalized population Wn=Zn/E[Zn[xi]] to its limit W[infinity]: we show a central limit theorem for W[infinity]-Wn with suitable normalization and derive a Berry-Esseen bound for the rate of convergence in the central limit theorem when the environment is independent and identically distributed. Similar results are also shown for Wn+k-Wn for each fixed .

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:539-547
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    Cited by:

    1. Zhang, Xiaoyue & Hong, Wenming, 2022. "Quenched convergence rates for a supercritical branching process in a random environment," Statistics & Probability Letters, Elsevier, vol. 181(C).
    2. 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).
    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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