Belyaev, M. Yu. 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.) Keywords:supercritical Markov branching process; convergence in distribution to a mixture of Gaussian laws Citations:Zbl 0181.211 PDFBibTeX XMLCite \textit{M. Yu. Belyaev}, Sov. Math., Dokl. 32, 188--190 (1985; Zbl 0613.60077); translation from Dokl. Akad. Nauk SSSR 283, 791--793 (1985)