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

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.

29 pages. In Section 2 we recall some notions and statements from arXiv:1403.0245