×

Some properties of a branching process with group immigration and emigration. (English) Zbl 0631.60083

This paper presents a model of a branching process with immigration and emigration which is related to a model studied by A. Tessera [J. Appl. Prob. 21, 225-232 (1984; Zbl 0537.92019)]. The model is more general in the sense that a random number of individuals (“founders”) enter the population and initiate collectively a tribe. Entrance times occur in accordance with a renewal process. Tribes, initiated at time \(T_ i\), say, are supposed to emigrate after some random sojourn time possibly depending on \(T_ i.\)
Let X(t) describe the number of inhabitants (in a given region) at time t. The article determines conditions under which X() has a limiting distribution. The limiting behaviour of X() is then studied for the case, when no limiting distribution exists, and it is compared with the corresponding model without emigration. Several criteria are determined according to assumptions on the family size and sojourn times and/or the immigration distribution.
Reviewer: F.Bruss

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60F05 Central limit and other weak theorems

Citations:

Zbl 0537.92019
PDFBibTeX XMLCite
Full Text: DOI