Abstract
Let (Z n ) be a supercritical branching process in an independent and identically distributed random environment ζ = (ζ 0, ζ 1,…), and let W be the limit of the normalized population size Z n /\(\mathbb{E}\)(Z n |ζ). We show a necessary and sufficient condition for the existence of weighted moments of W of the form \(\mathbb{E}\), where α ≥ 1 and ℓ is a positive function slowly varying at ∞.
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Liang, X., Liu, Q. Weighted moments of the limit of a branching process in a random environment. Proc. Steklov Inst. Math. 282, 127–145 (2013). https://doi.org/10.1134/S0081543813060126
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DOI: https://doi.org/10.1134/S0081543813060126