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.
Highlights
Academic Editors: Panagiotis-Christos Vassiliou and Andreas C
We find the form of the differential equation and the generating function for the random process, which describes the behavior of the process within the PL
We find a differential equation for the probability generating functions (PGFs) and PGF random process, which describes the behavior of the process within the PL of the branching process with migration and continuous time (BPMCT)
Summary
Academic Editors: Panagiotis-Christos Vassiliou and Andreas C. Branching processes (BPs) are often used as mathematical models of different real processes, in particular, chemical [1], biological [2], genetic [3], demographic [4], technical [5]. BPs can describe the population dynamics of particles of different natures, in particular, they can be photons, electrons, neutrons, protons, atoms, molecules, cells, microorganisms, plants, animals, individuals, prices, information, etc. Among them are BPs with immigration, emigration, or a combination of two processes, namely processes with migration for the case of discrete or continuous time
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