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Branching processes in periodically varying environment. (English) Zbl 0557.60072

The general branching process counted by a random characteristic has been studied extensively by both authors in recent years [e.g. Adv. Appl. Probab. 16, 221-259 (1984; Zbl 0535.60075)]. The concept of reproductive behaviour depending periodically on time has been considered by a number of authors, notably B. Klein and P. D. M. MacDonald, [ibid. 12, 81-93 (1980; Zbl 0421.60076).
In the present paper the authors superimpose such periodic behaviour on their own general one-type branching process. Under certain second moment restrictions, the authors obtain conditions for a Malthusian parameter to exist, a martingale determining the growth of the process on the event of non-extinction under these conditions, and a periodically varying asymptotic stable age distribution. The intended application is to the diurnal variation of cell population growth.
Reviewer: D.R.Grey

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J85 Applications of branching processes
92D25 Population dynamics (general)
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