Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration
Probability
2016-07-25 v3
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.
Keywords
Cite
@article{arxiv.1404.2242,
title = {Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration},
author = {Matyas Barczy and Gyula Pap},
journal= {arXiv preprint arXiv:1404.2242},
year = {2016}
}
Comments
29 pages. In Section 2 we recall some notions and statements from arXiv:1403.0245