Geometric rate of growth in population-size-dependent branching processes. (English) Zbl 0544.60073

Klebaner, F. C.

J. Appl. Probab. 21, 40-49 (1984).

”We consider a branching process model \(\{Z_ n\}\), where the law of offspring distribution depends on the population size. We consider the case when the means \(m_ n (m_ n\) is the mean of offspring distribution when the population size is equal to n) tend to a limit \(m>1\) as \(n\to \infty\). For a certain class of processes \(\{Z_ n\}\) necessary conditions for convergence in \(L^ 1\) and \(L^ 2\) and sufficient conditions for almost sure convergence and convergence in \(L^ 2\) of \(W_ n=Z_ n/m^ n\) are given”. (Author’s summary)
This paper appears to be a postscript to a more substantial one by the same author, Adv. Appl. Probab. 16, 30-55 (1984; Zbl 0528.60080).

Reviewer: D.R.Grey

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60F15	Strong limit theorems
60F25	\(L^p\)-limit theorems

Keywords:

branching process model; conditions for convergence