Weighted moments of the limit of a branching process in a random environment
Résumé
Let $(Z_n)$ be a supercritical branching process in an independent and identically distributed random environment $\zeta =(\zeta _{0},\zeta _{1},\ldots )$, and let $W$ be the limit of the normalized population size $Z_n/\mathbb{E}(Z_n|\zeta)$. We show a necessary and sufficient condition 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 the corresponding ones of Bingham and Doney (1974) and Alsmeyer and Rösler (2004).
Domaines
Probabilités [math.PR]
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liang_liu_Weighted_momemt_BPRE_nov2012_revised.pdf (233.76 Ko)
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