naa a22 4500 510812023 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060151 doi (NATIONALLICENCE)springer-10.1134/S0081543813060151 Sevastyanov branching processes with non-homogeneous Poisson immigration [Elektronische Daten] [Kosto Mitov, Nickolay Yanev] 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. Pleiades Publishing, Ltd., 2013 Mitov Kosto Faculty of Aviation, Vasil Levski National Military University, 5856, D. Mitropolia, Pleven, Bulgaria aut Yanev Nickolay Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 172-185 0081-5438 282:1<172 2013 282 11501 https://doi.org/10.1134/S0081543813060151 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060151 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mitov Kosto Faculty of Aviation, Vasil Levski National Military University, 5856, D. Mitropolia, Pleven, Bulgaria aut NATIONALLICENCE 700 1- Yanev Nickolay Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 172-185 0081-5438 282:1<172 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer