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

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 individ...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-04, Vol.9 (8), p.868
Main Authors: Prysyazhnyk, Khrystyna, Bazylevych, Iryna, Mitkova, Ludmila, Ivanochko, Iryna
Format: Article
Language:English
Subjects:
Branching (mathematics)
branching process
continuous time
Emigration
generating function
Immigration
Markov processes
Mathematics
Migration
Noncitizens
period-life
Random processes
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9080868