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Weighted moments of the limit of a branching process in a random environment
- Publication Year :
- 2010
-
Abstract
- 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).<br />Comment: 16 pages
- Subjects :
- Mathematics - Probability
60K37, 60J80
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1007.1869
- Document Type :
- Working Paper