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.
ISSN 2351-6054
(Unpublished)
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: |
01 Sep 2020 12:54 |
| Last Modified: |
01 Sep 2020 12:54 |
| URI: |
http://real.mtak.hu/id/eprint/112634 |
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On tail behaviour of stationary second-order Galton-Watson processes with immigration. (deposited 01 Sep 2020 12:54)
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