On the Kolmogorov constant explicit form in the theory of discrete-time stochastic branching systems

On the Kolmogorov constant explicit form in the theory of discrete-time stochastic branching systems

We consider a discrete-time population growth system called the Bienaymé–Galton–Watson stochastic branching system. We deal with a noncritical case, in which the per capita offspring mean $m\neq1$ . The famous Kolmogorov theorem asserts that the expectation of the population size in the subcritical...

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Veröffentlicht in:Journal of applied probability 2024-09, Vol.61 (3), p.927-941
Hauptverfasser: Imomov, Azam A., Murtazaev, Misliddin S.
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic methods
Asymptotic properties
Asymptotic series
Basic converters
Discrete time systems
Extinction
Original Article
Population growth
Probability
Theorems
Transition probabilities
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Zusammenfassung:We consider a discrete-time population growth system called the Bienaymé–Galton–Watson stochastic branching system. We deal with a noncritical case, in which the per capita offspring mean $m\neq1$ . The famous Kolmogorov theorem asserts that the expectation of the population size in the subcritical case $m
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2023.85