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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
\serial Trudy Mat. Inst. Steklova
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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:
    1. Kosto V. Mitov, Nikolay M. Yanev, “Critical Markov branching process with infinite variance allowing Poisson immigration with increasing intensity”, Stochastic Analysis and Applications, 42:4 (2024), 828  crossref
    2. Maroussia Slavtchova-Bojkova, Ollivier Hyrien, Nikolay M. Yanev, “Subcritical multitype Markov branching processes with immigration generated by Poisson random measures”, Communications in Statistics - Theory and Methods, 2023, 1  crossref
    3. Slavtchova-Bojkova M., Hyrien O., Yanev N.M., “Poisson Random Measures and Supercritical Multitype Markov Branching Processes”, Stoch. Models, 2022  crossref  mathscinet  isi
    4. Slavtchova-Bojkova M.N., Hyrien O., Yanev N.M., “Poisson Random Measures and Noncritical Multitype Markov Branching Processes”, C. R. Acad. Bulg. Sci., 74:5 (2021), 658–668  crossref  mathscinet  isi
    5. Ibrahim Rahimov, “Homogeneous Branching Processes with Non-Homogeneous Immigration”, Stochastics and Quality Control, 36:2 (2021), 165  crossref
    6. Mitov V K., “Critical Markov Branching Processes With Non-Homogeneous Poisson Immigration”, C. R. Acad. Bulg. Sci., 73:7 (2020), 908–914  crossref  mathscinet  isi
    7. Slavtchova-Bojkova M., Yanev N.M., “Poisson Random Measures and Critical Sevastyanov Branching Processes”, Stoch. Models, 35:2 (2019), 197–208  crossref  mathscinet  isi  scopus
    8. K. V. Mitov, N. M. Yanev, O. Hyrien, “Multitype branching processes with inhomogeneous Poisson immigration”, Adv. Appl. Probab., 50:A (2018), 211–228  crossref  mathscinet  isi  scopus
    9. N. M. Yanev, O. Hyrien, K. V. Mitov, “Limiting distributions for multitype Markov branching processes with non-homogeneous Poisson immigration”, C. R. Acad. Bulg. Sci., 70:12 (2017), 1627–1634  mathscinet  zmath  isi
    10. O. Hyrien, K. V. Mitov, N. M. Yanev, “Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration”, J. Appl. Probab., 54:2 (2017), 569–587  crossref  mathscinet  isi  scopus
    11. K. V. Mitov, N. M. Yanev, “Limiting distributions for alternating regenerative branching processes”, C. R. Acad. Bulg. Sci., 69:10 (2016), 1251–1262  mathscinet  zmath  isi
    12. O. Hyrien, K. V. Mitov, N. M. Yanev, “Supercritical Sevastyanov branching processes with non-homogeneous Poisson immigration”, Branching Processes and Their Applications, Lecture Notes in Statistics, 219, eds. I. DelPuerto, M. Gonzalez, C. Gutierrez, R. Martinez, C. Minuesa, M. Molina, M. Mota, A. Ramos, Springer, 2016, 151–166  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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