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

Abstract

Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: On tail behaviour of stationary second-order Galton–Watson processes with immigration, Authors: Mátyás Barczy, Zsuzsanna Bősze, Gyula Pap , Sufficient conditions are presented on the offspring and immigration distributions of a second-order Galton–Watson process ${({X_{n}})_{n\geqslant -1}}$ with immigration, under which the distribution of the initial values $({X_{0}},{X_{-1}})$ can be uniquely chosen such that the process becomes strongly stationary and the common distribution of ${X_{n}}$, $n\geqslant -1$, is regularly varying.