On tail behaviour of stationary second-order Galton-Watson processes with immigration
arXiv:1801.07931 · doi:10.15559/20-VMSTA161
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.
43 pages. arXiv admin note: text overlap with arXiv:1805.00820