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Period-Life of a Branching Process with Migration and Continuous Time

Author

Listed:
  • Khrystyna Prysyazhnyk

    (Artificial Intelligence Department, Institute of Computer Sciences and Information Technologies, Lviv Polytechnic National University, 79013 Lviv, Ukraine)

  • Iryna Bazylevych

    (Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine)

  • Ludmila Mitkova

    (Department of Economics and Finance, Comenius University, 82005 Bratislava, Slovakia)

  • Iryna Ivanochko

    (Department of Management and International Business, Lviv Polytechnic National University, 79000 Lviv, Ukraine)

Abstract

The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ , i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found.

Suggested Citation

  • Khrystyna Prysyazhnyk & Iryna Bazylevych & Ludmila Mitkova & Iryna Ivanochko, 2021. "Period-Life of a Branching Process with Migration and Continuous Time," Mathematics, MDPI, vol. 9(8), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:868-:d:536370
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    References listed on IDEAS

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    1. Chen, Anyue & Renshaw, Eric, 1995. "Markov branching processes regulated by emigration and large immigration," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 339-359, June.
    2. V. A. Dimitriou & A. C. Georgiou, 2021. "Introduction, analysis and asymptotic behavior of a multi-level manpower planning model in a continuous time setting under potential department contraction," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(5), pages 1173-1199, March.
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