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arXiv · 1404.2242

Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration

Matyas Barczy·Gyula Pap
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Abstract

Under natural assumptions, a Feller type diffusion approximation is derived for critical, irreducible multi-type continuous state and continuous time branching processes with immigration. Namely, it is proved that a sequence of appropriately scaled random step functions formed from a critical, irreducible multi-type continuous state and continuous time branching process with immigration converges weakly towards a squared Bessel process supported by a ray determined by the Perron vector of a matrix related to the branching mechanism of the branching process in question.

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Matyas Barczy, Gyula Pap. 2015-06-17. Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration. https://arxiv.org/abs/1404.2242

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