Journal
MATHEMATICS
Volume 9, Issue 8, Pages -Publisher
MDPI
DOI: 10.3390/math9080868
Keywords
branching process; migration; continuous time; generating function; period-life
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The study focuses on the homogeneous branching process with migration and continuous time, investigating the distribution of period-life tau and obtaining the probability generating function of the random process. Additionally, the boundary theorem for the period-life of the subcritical or critical branching process with migration was identified.
The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life tau, 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.
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