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Convergence of functionals of supercritical Markov branching processes. (English. Russian original) Zbl 0613.60077

Sov. Math., Dokl. 32, 188-190 (1985); translation from Dokl. Akad. Nauk SSSR 283, 791-793 (1985).
The supercritical Markov branching process taking values in the space of finite measures over a complete separable metric space X is considered. Under appropriate moment conditions, results are presented (without proofs) on the convergence as \(t\to \infty\) of normalized linear functionals of the random measure \(\mu_ t\) which represents the population size at time t. The types of convergence are mean square convergence to a random variable and convergence in distribution to a mixture of Gaussian laws, as originally discovered in the case of finite X by K. B. Athreya [Z. Wahrscheinlichkeitstheor. Verw. Geb. 12, 320-332 and 13, 204-214 (1969; Zbl 0181.211)].
Reviewer: D.R.Grey

MSC:

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

Citations:

Zbl 0181.211
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