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.
Accepté le :
DOI : 10.1051/ps/2016010
Mots-clés : Critical multi-type branching processes with immigration, squared Bessel processes
@article{PS_2016__20__238_0,
author = {Danka, Tivadar and Pap, Gyula},
title = {Asymptotic behavior of critical indecomposable multi-type branching processes with immigration},
journal = {ESAIM: Probability and Statistics},
pages = {238--260},
publisher = {EDP-Sciences},
volume = {20},
year = {2016},
doi = {10.1051/ps/2016010},
mrnumber = {3528626},
zbl = {1356.60129},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2016010/}
}
TY - JOUR AU - Danka, Tivadar AU - Pap, Gyula TI - Asymptotic behavior of critical indecomposable multi-type branching processes with immigration JO - ESAIM: Probability and Statistics PY - 2016 SP - 238 EP - 260 VL - 20 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2016010/ DO - 10.1051/ps/2016010 LA - en ID - PS_2016__20__238_0 ER -
%0 Journal Article %A Danka, Tivadar %A Pap, Gyula %T Asymptotic behavior of critical indecomposable multi-type branching processes with immigration %J ESAIM: Probability and Statistics %D 2016 %P 238-260 %V 20 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2016010/ %R 10.1051/ps/2016010 %G en %F PS_2016__20__238_0
Danka, Tivadar; Pap, Gyula. Asymptotic behavior of critical indecomposable multi-type branching processes with immigration. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 238-260. doi : 10.1051/ps/2016010. http://archive.numdam.org/articles/10.1051/ps/2016010/
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