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On some classes of population-size-dependent Galton-Watson processes. (English) Zbl 0573.60079
For some classes of population-size-dependent Galton-Watson processes $$\{Z(t)\}_{t=0,1,...}$$, criteria for almost certain extinction are obtained. Gamma-type limit distributions of Z(t)/t as $$t\to \infty$$ are found to hold in cases where extinction does not occur with probability one. The results can be stated under conditions on moments of the underlying reproduction distributions; the proofs make use of functional iteration tools.

##### MSC:
 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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