On tail behaviour of stationary second-order Galton-Watson processes with immigration

Barczy, Mátyás and Bősze, Zsuzsanna and Pap, Gyula (2020) On tail behaviour of stationary second-order Galton-Watson processes with immigration. Modern Stochastics: Theory and Applications, 7 (3). pp. 315-338. ISSN 2351-6054

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Abstract

A second-order Galton-Watson process with immigration can be represented as a coordinate process of a 2-type Galton-Watson process with immigration. Sufficient conditions are derived on the offspring and immigration distributions of a second-order Galton-Watson process with immigration under which the corresponding 2-type Galton-Watson process with immigration has a unique stationary distribution such that its common marginals are regularly varying. In the course of the proof sufficient conditions are given under which the distribution of a second-order Galton-Watson process (without immigration) at any fixed time is regularly varying provided that the initial sizes of the population are independent and regularly varying.

Item Type:	Article
Additional Information:	Supported by the Hungarian Croatian Intergovernmental S&T Cooperation Programme for 2017-2018 under Grant No. 16-1-2016-0027. Mátyás Barczy is supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
Uncontrolled Keywords:	second-order Galton–Watson process with immigration, regularly varying distribution, tail behavior
Subjects:	Q Science / természettudomány > QA Mathematics / matematika
Depositing User:	Dr Mátyás Barczy
Date Deposited:	08 Mar 2021 15:44
Last Modified:	03 Apr 2023 07:09
URI:	http://real.mtak.hu/id/eprint/122014

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• On tail behaviour of stationary second-order Galton-Watson processes with immigration. (deposited 01 Sep 2020 12:54)
  • On tail behaviour of stationary second-order Galton-Watson processes with immigration. (deposited 08 Mar 2021 15:44) [Currently Displayed]

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