Barczy, Mátyás and Kunosné Nedényi, Fanni and Pap, Gyula
(2020)
On aggregation of subcritical Galton-Watson branching processes with regularly varying immigration.
Lithuanian Mathematical Journal.
ISSN 0363-1672 (print), 1573-8825 (online)
(Unpublished)
Abstract
We study an iterated temporal and contemporaneous aggregation of N independent copies of a strongly stationary subcritical Galton-Watson branching process with regularly varying immigration having index α in (0,2). Limits of finite dimensional distributions of appropriately centered and scaled aggregated partial sum processes are shown to exist when first taking the limit as N tends to infinity and then the time scale n tends to infinity. The limit process is an α-stable process if α is in (0,1)∪(1,2), and a deterministic line with slope 1 if α=1.
| Item Type: |
Article
|
| Additional Information: |
Mátyás Barczy is supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. Fanni K. Nedényi is supported by the UNKP-18-3 New National Excellence Program of the Ministry of
Human Capacities. Gyula Pap was supported by the Ministry for Innovation and Technology, Hungary grant TUDFO/47138-1/2019-ITM. |
| Uncontrolled Keywords: |
Galton–Watson branching processes with immigration, temporal and contemporaneous aggregation, multivariate regular variation, stable distribution, limit measure, tail process |
| Subjects: |
Q Science / természettudomány > QA Mathematics / matematika |
| Depositing User: |
Dr Mátyás Barczy
|
| Date Deposited: |
01 Sep 2020 13:05 |
| Last Modified: |
01 Sep 2020 13:05 |
| URI: |
http://real.mtak.hu/id/eprint/112636 |
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On aggregation of subcritical Galton-Watson branching processes with regularly varying immigration. (deposited 01 Sep 2020 13:05)
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