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