On tail behaviour of stationary second-order Galton-Watson processes with immigration
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.
Keywords
Cite
@article{arxiv.1801.07931,
title = {On tail behaviour of stationary second-order Galton-Watson processes with immigration},
author = {Matyas Barczy and Zsuzsanna Bősze and Gyula Pap},
journal= {arXiv preprint arXiv:1801.07931},
year = {2020}
}
Comments
43 pages. arXiv admin note: text overlap with arXiv:1805.00820