Abstract:
For multitype branching processes with immigration evolving in a random environment and producing a final product, we find the tail distribution of the size of the final product accumulated in the process for a life period. Using this result, we investigate the tail distributions of the busy periods of the queueing polling systems of branching type with random service disciplines and random positive switch-over times.
Key words:
subcritical branching processes with immigration, final product, random environment, limit theorems, polling systems, busy period.
Citation:
V. A. Vatutin, “Multitype branching processes with immigration in random environment, and polling systems”, Mat. Tr., 14:1 (2011), 3–49; Siberian Adv. Math., 21:1 (2011), 42–72
\Bibitem{Vat11}
\by V.~A.~Vatutin
\paper Multitype branching processes with immigration in random environment, and polling systems
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 1
\pages 3--49
\mathnet{http://mi.mathnet.ru/mt205}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2858652}
\elib{https://elibrary.ru/item.asp?id=16441654}
\transl
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 1
\pages 42--72
\crossref{https://doi.org/10.3103/S1055134411010020}
\elib{https://elibrary.ru/item.asp?id=17002950}
Linking options:
https://www.mathnet.ru/eng/mt205
https://www.mathnet.ru/eng/mt/v14/i1/p3
This publication is cited in the following 14 articles:
Xulan Huang, “Quenched weighted moments for a branching process with immigration in a random environment”, Stochastic Models, 40:2 (2024), 278
Manuel Molina-Fernández, Manuel Mota-Medina, “Parametric Inference in Biological Systems in a Random Environment”, Axioms, 13:12 (2024), 883
Xiaoqiang Wang, Chunmao Huang, “Moments, large and moderate deviations for branching random walks with immigration in random environments”, Journal of Mathematical Analysis and Applications, 523:1 (2023), 126993
Huang Ch., Wang Ch., Wang X., “Moments and Large Deviations For Supercritical Branching Processes With Immigration in Random Environments”, Acta Math. Sci., 42:1 (2022), 49–72
Xulan Huang, Yingqiu Li, Kainan Xiang, “Berry–Esseen bound for a supercritical branching processes with immigration in a random environment”, Statistics & Probability Letters, 190 (2022), 109619
Yingqiu Li, Xulan Huang, “A.s. convergence rate for a supercritical branching processes with immigration in a random environment”, Communications in Statistics - Theory and Methods, 51:3 (2022), 826
Yingqiu Li, Xulan Huang, Zhaohui Peng, “Central Limit Theorem and Convergence Rates for a Supercritical Branching Process with Immigration in a Random Environment”, Acta Math Sci, 42:3 (2022), 957
V. A. Vatutin, E. E. Dyakonova, “Multitype branching processes in random environment”, Russian Math. Surveys, 76:6 (2021), 1019–1063
Molina-Fernandez M., Mota-Medina M., “Demographic Dynamics in Multitype Populations With Migrations”, Mathematics, 9:3 (2021), 246
Vishnevsky V., Semenova O., “Polling Systems and Their Application to Telecommunication Networks”, Mathematics, 9:2 (2021), 117
Bansaye V., Camanes A., “Queueing For An Infinite Bus Line and Aging Branching Process”, Queueing Syst., 88:1-2 (2018), 99–138
Zerner M.P.W., “Recurrence and Transience of Contractive Autoregressive Processes and Related Markov Chains”, Electron. J. Probab., 23 (2018), 27
Discrete Time Branching Processes in Random Environment, 2017, 275
E. E. D'yakonova, “Multitype branching processes evolving in a Markovian environment”, Discrete Math. Appl., 22:5-6 (2012), 639–664
Citation in format AMSBIB
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