TRANSIENT PHENOMENA FOR TOTAL PROGENYIN GALTON–WATSON PROCESSES WITH IMMIGRATION

Galton–Watson branching processes with immigration are considered, in which the mathematical expectation A of the number of offspring of a single individual tends towards unity. For the process denoting the number of individuals that existed before generation n (total progeny), normalized by mathematical expectation, an asymptotic distribution has been found that depends on the rate at which A tends towards unity. Keywords: branching processes with immigration, total progeny, transient phenomena.

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Publication Details

Journal
Kibernetyka ta Systemnyi Analiz
Published
2025-01-01
DOI
https://doi.org/10.34229/kca2522-9664.25.2.10
Primary Topic
Solidification and crystal growth phenomena
Type
article
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article

TRANSIENT PHENOMENA FOR TOTAL PROGENYIN GALTON–WATSON PROCESSES WITH IMMIGRATION

Ya. I. Yeleiko, T. B. Lysetskyi
Kibernetyka ta Systemnyi Analiz
Solidification and crystal growth phenomena
article

TRANSIENT PHENOMENA FOR TOTAL PROGENYIN GALTON–WATSON PROCESSES WITH IMMIGRATION

Ya. I. Yeleiko, T. B. Lysetskyi
article en

Abstract

Galton–Watson branching processes with immigration are considered, in which the mathematical expectation A of the number of offspring of a single individual tends towards unity. For the process denoting the number of individuals that existed before generation n (total progeny), normalized by mathematical expectation, an asymptotic distribution has been found that depends on the rate at which A tends towards unity. Keywords: branching processes with immigration, total progeny, transient phenomena.

Kibernetyka ta Systemnyi Analiz
Openalex Percentile: Top 96%
Solidification and crystal growth phenomena
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TRANSIENT PHENOMENA FOR TOTAL PROGENYIN GALTON–WATSON PROCESSES WITH IMMIGRATION — Ya. I. Yeleiko, T. B. Lysetskyi · Kibernetyka ta Systemnyi Analiz (2025) | TGRS Research Map | TGRS