Limit theorems for a branching process with variable regime. (English. Russian original) Zbl 0633.60095

Bojko, R. V.

Theory Probab. Math. Stat. 35, 5-11 (1987); translation from Teor. Veroyatn. Mat. Stat. 35, 6-13 (1986).

A continuous time Markov branching process is modified so that the transformation intensity per head depends on current population size. Limit theorems are obtained under conditions which ensure that this intensity is asymptotically inversely proportional to population size.
These conditions mean that the process is more akin to a compound Poisson process than to a branching process and it is therefore not surprising (although not acknowledged by the author) that this kinship is reflected in the nature of the limit theorems: for example, linear growth in the supercritical case. The paper is a sequel to earlier ones by the same author, see Ukr. Math. Zh. 34, No.6, 681-687 (1982; Zbl 0563.60076); English translation in Ukr. Math. J. 34, 549-554 (1983).

Reviewer: D.R.Grey

MSC:

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

Keywords:

continuous time Markov branching process; Limit theorems; population size; linear growth in the supercritical case

Citations:

Zbl 0563.60076