Renewed Limit Theorems for Noncritical Galton–Watson Branching Systems

Azam A. Imomov () and Misliddin Murtazaev ()
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Azam A. Imomov: Karshi State University
Misliddin Murtazaev: V.I.Romanovskiy Institute of Mathematics

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2843-2858

Abstract: Abstract The paper discusses the Galton–Watson stochastic branching system. We deal only with the noncritical case. Our task in the work is to improve our recent result which explicitly calculated the famous constant in the theory of subcritical Galton–Watson branching systems, announced by Kolmogorov in 1938. We demonstrate the rate of convergence to the Kolmogorov constant. This improvement contributes to determining the speed of approximation rate in a number of classical limit theorems of the theory of Galton–Watson branching systems.

Keywords: Galton–Watson branching system; Markov chain; Extinction time; Kolmogorov constant; Basic Lemma; Invariant distribution; Limit theorems; Convergence rate; 60J80; 60J85 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01330-8

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