Volume 20, 2016
|Page(s)||238 - 260|
|Published online||18 July 2016|
Asymptotic behavior of critical indecomposable multi-type branching processes with immigration∗
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged,
Revised: 9 December 2015
Accepted: 10 March 2016
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 matrix. The types can be partitioned into nonempty mutually disjoint subsets (according to communication of types) such that the coordinate processes belonging to the same subset are multiples of the same squared Bessel process, and the coordinate processes belonging to different subsets are independent.
Mathematics Subject Classification: 60J80 / 60F17 / 60J60
Key words: Critical multi-type branching processes with immigration / squared Bessel processes
The research of T. Danka and G. Pap was realized in the frames of TÁMOP 4.2.4. A/2-11-1-2012-0001 ’National Excellence Program – Elaborating and operating an inland student and researcher personal support system’. The project was subsidized by the European Union and co-financed by the European Social Fund.
© EDP Sciences, SMAI, 2016
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