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Multitype branching process with non-homogeneous Poisson and contagious Poisson immigration
Published online by Cambridge University Press: 22 November 2021
Abstract
In a multitype branching process, it is assumed that immigrants arrive according to a non-homogeneous Poisson or a contagious Poisson process (both processes are formulated as a non-homogeneous birth process with an appropriate choice of transition intensities). We show that the normalized numbers of objects of the various types alive at time t for supercritical, critical, and subcritical cases jointly converge in distribution under those two different arrival processes. Furthermore, we provide some transient expectation results when there are only two types of particles.
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust
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