Geodesic
Asymptotic behavior of critical indecomposable multi-type branching processes with immigration
Danka, Tivadar1 ; Pap, Gyula1
1 Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 238-260

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016010
Classification : 60J80, 60F17, 60J60
Keywords: Critical multi-type branching processes with immigration, squared Bessel processes

Danka, Tivadar 1 ; Pap, Gyula 1

1 Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary. 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :