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arXiv · 1801.07931

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

Matyas Barczy·Zsuzsanna Bősze·Gyula Pap
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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.

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Matyas Barczy, Zsuzsanna Bősze, Gyula Pap. 2018-01-24. On tail behaviour of stationary second-order Galton-Watson processes with immigration. https://doi.org/10.15559/20-vmsta161

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