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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 282, Pages 181–194
DOI: https://doi.org/10.1134/S0371968513030151 (Mi tm3491) 		 
This article is cited in 12 scientific papers (total in 12 papers)

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
Full-text PDF (219 kB) Citations (12)
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DOI: https://doi.org/10.1134/S0371968513030151
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.
Received in January 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 282, Pages 172–185
DOI: https://doi.org/10.1134/S0081543813060151
Bibliographic databases:
Document Type: Article
UDC: 519.218.24
Language: English
Citation: Kosto V. Mitov, Nikolay M. Yanev, “Sevastyanov branching processes with non-homogeneous Poisson immigration”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 181–194; Proc. Steklov Inst. Math., 282 (2013), 172–185
Citation in format AMSBIB
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\paper Sevastyanov branching processes with non-homogeneous Poisson immigration
\inbook Branching processes, random walks, and related problems
\bookinfo Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences
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\vol 282
\pages 181--194
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 12 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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