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Weighted moments for a supercritical branching process in a varying or random environment

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Abstract

Let W be the limit of the normalized population size of a supercritical branching process in a varying or random environment. By an elementary method, we find sufficient conditions under which W has finite weighted moments of the form EW p l(W), where p > 1, l ⩾ 0 is a concave or slowly varying function.

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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, YangLi Hu & QuanSheng Liu

  2. College of Mathematics and Computer Sciences, Hunan Normal University, Changsha, 410081, China

    YingQiu Li & YangLi Hu

  3. LMAM, University of Bretgne-Sud, BP573, 56017, Vannes, France

    QuanSheng Liu

Authors
  1. YingQiu Li
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  2. YangLi Hu
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  3. QuanSheng Liu
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Correspondence to QuanSheng Liu.

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Li, Y., Hu, Y. & Liu, Q. Weighted moments for a supercritical branching process in a varying or random environment. Sci. China Math. 54, 1437–1444 (2011). https://doi.org/10.1007/s11425-011-4220-y

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  • DOI: https://doi.org/10.1007/s11425-011-4220-y

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