| Issue |
ESAIM: PS
Volume 28, 2024
|
|
|---|---|---|
| Page(s) | 350 - 365 | |
| DOI | https://doi.org/10.1051/ps/2024011 | |
| Published online | 21 November 2024 | |
Ergodic properties of subcritical multitype Galton–Watson processes with immigration
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
* Corresponding author: szucsg@math.u-szeged.hu
Received:
31
December
2023
Accepted:
13
July
2024
In the paper ergodic properties of multitype Galton–Watson processes are investigated in the subcritical case without further regularity assumptions. Sufficient and necessary conditions for the existence of the stationary distribution and its moments are provided. Under moment conditions geometric ergodicity and rate of converge for the moments of the process are proved. Geometric properties of the Markovian class structure are also studied.
Mathematics Subject Classification: 60J80 / 60G10
Key words: Galton–Watson processes / Multitype branching processes / Stationary distribution / Geometric ergodicity
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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