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Sevastyanov branching processes with non-homogeneous Poisson immigration

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Abstract

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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Authors and Affiliations

  1. Faculty of Aviation, Vasil Levski National Military University, 5856, D. Mitropolia, Pleven, Bulgaria

    Kosto V. Mitov

  2. Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Nickolay M. Yanev

Authors
  1. Kosto V. Mitov
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  2. Nickolay M. Yanev
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Correspondence to Kosto V. Mitov.

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Mitov, K.V., Yanev, N.M. Sevastyanov branching processes with non-homogeneous Poisson immigration. Proc. Steklov Inst. Math. 282, 172–185 (2013). https://doi.org/10.1134/S0081543813060151

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  • DOI: https://doi.org/10.1134/S0081543813060151

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