Weighted moments of the limit of a branching process in a random environment
Liang, Xingang · Liu, Quansheng
Original · EN
Let (Zₙ) be a supercritical branching process in a random environment % ζ, and W be the limit of the normalized population size Zₙ/E%(Zₙ|ζ). We show necessary and sufficient conditions for the existence of weighted moments of W of the form Wαℓ(W), where α≥ 1, ℓ is a positive function slowly varying at ∞. In the Galton-Watson case, the results improve those of Bingham and Doney (1974).
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