Sevastyanov branching processes with non-homogeneous Poisson immigration

被引：0
|
作者：
Kosto V. Mitov
Nickolay M. Yanev
机构：
[1] Vasil Levski National Military University,Faculty of Aviation
[2] Bulgarian Academy of Sciences,Department of Probability and Statistics, Institute of Mathematics and Informatics
来源：
Proceedings of the Steklov Institute of Mathematics | 2013年 / 282卷
关键词：
Limit Theorem; STEKLOV Institute; Critical Case; Jump Point; Mean Value Theorem;
D O I：
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学科分类号：
摘要：
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.
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页码：172 / 185
页数：13
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