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

Barczy, Mátyás and Pap, Gyula (2016) Asymptotic behavior of critical, irreducible multi-type continuous state and continuous time branching processes with immigration. STOCHASTICS AND DYNAMICS, 16 (4). ISSN 0219-4937

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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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