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Asymptotic properties of supercritical branching processes in random environments

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Abstract

We consider a supercritical branching process (Z n ) in an independent and identically distributed random environment ξ, and present some recent results on the asymptotic properties of the limit variable W of the natural martingale W n = Z n /\(\mathbb{E}\)[Z n |ξ], the convergence rates of W − W n (by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in L p, and the convergence in probability), and limit theorems (such as central limit theorems, moderate and large deviations principles) on (log Z n ).

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Authors and Affiliations

  1. College of Mathematics and Computing Sciences, Changsha University of Science and Technology, Changsha, 410004, China

    Yingqiu Li, Quansheng Liu & Hesong Wang

  2. Université de Bretagne-Sud, UMR 6205, LMBA, F-56000, Vannes, France

    Quansheng Liu

  3. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Zhiqiang Gao

Authors
  1. Yingqiu Li
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  2. Quansheng Liu
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  3. Zhiqiang Gao
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  4. Hesong Wang
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Correspondence to Quansheng Liu.

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Li, Y., Liu, Q., Gao, Z. et al. Asymptotic properties of supercritical branching processes in random environments. Front. Math. China 9, 737–751 (2014). https://doi.org/10.1007/s11464-014-0397-z

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  • DOI: https://doi.org/10.1007/s11464-014-0397-z

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