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Asymptotic behavior of critical indecomposable multi-type branching processes with immigration

2016
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E S A I M: Probability & Statistics
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In this paper the asymptotic behavior of a critical multi-type branching process with immigration is described when the offspring mean matrix is irreducible, in other words, when the process is indecomposable. It is proved that sequences of appropriately scaled random step functions formed from periodic subsequences of a critical indecomposable multi-type branching process with immigration converge weakly towards a process supported by a ray determined by the Perron vector of the offspring mean

doi:10.1051/ps/2016010
fatcat:rp4sr37amvfinm2fthaecwme4a