Weighted moments of the limit of a branching process in a random environment

Details Weighted moments of the limit of a branching process in a random environment Weighted moments of the limit of a branching process in a random environment

2010-07-12

arxiv.org/abs/1007.1869v1

Mathematics

Probability

16 pages

Scientific paper

Let $(Z_n)$ be a supercritical branching process in a random environment $% \zeta$, and $W$ be the limit of the normalized population size $Z_n/\mathbb{E%}(Z_n|\zeta)$. We show necessary and sufficient conditions for the existence of weighted moments of $W$ of the form $\E W^{\alpha}\ell(W)$, where $\alpha\geq 1$, $\ell$ is a positive function slowly varying at $\infty$. In the Galton-Watson case, the results improve those of Bingham and Doney (1974).

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