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ЖУРНАЛЫ // Труды Математического института имени В. А. Стеклова // Архив

Труды МИАН, 2013, том 282, страницы 181–194 (Mi tm3491)

Эта публикация цитируется в 12 статьях

Sevastyanov branching processes with non-homogeneous Poisson immigration

Kosto V. Mitova, Nikolay M. Yanevb

a Faculty of Aviation, Vasil Levski National Military University, Pleven, Bulgaria
b Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

Аннотация: Sevastyanov age-dependent branching processes allowing an immigration component are considered in the case when the moments of immigration form a non-homogeneous Poisson process with intensity $r(t)$. The asymptotic behavior of the expectation and of the probability of non-extinction is investigated in the critical case depending on the asymptotic rate of $r(t)$. Corresponding limit theorems are also proved using different types of normalization. Among them we obtained limiting distributions similar to the classical ones of Yaglom (1947) and Sevastyanov (1957) and also discovered new phenomena due to the non-homogeneity.

УДК: 519.218.24

Поступило в январе 2013 г.

Язык публикации: английский

DOI: 10.1134/S0371968513030151


 Англоязычная версия: Proceedings of the Steklov Institute of Mathematics, 2013, 282, 172–185

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