On aggregation of subcritical Galton-Watson branching processes with regularly varying immigration

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, 60 (4). pp. 425-451. ISSN 0363-1672 (print), 1573-8825 (online)

Preview	Text Barczy_Nedenyi_Pap_202+_1.pdf Download (469kB) | Preview
	Text Barczy_Nedenyi_Pap.pdf - Published Version Restricted to Repository staff only Download (507kB) | Request a copy

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:	08 Mar 2021 15:46
Last Modified:	03 Apr 2023 07:09
URI:	http://real.mtak.hu/id/eprint/122013

Available Versions of this Item

• On aggregation of subcritical Galton-Watson branching processes with regularly varying immigration. (deposited 01 Sep 2020 13:05)
  • On aggregation of subcritical Galton-Watson branching processes with regularly varying immigration. (deposited 08 Mar 2021 15:46) [Currently Displayed]

Actions (login required)

Edit Item