On tail behaviour of stationary second-order Galton–Watson processes with immigration
Volume 7, Issue 3 (2020), pp. 315–338
Pub. online: 10 September 2020
Type: Research Article
Open Access
Open Access
Received
23 July 2020
23 July 2020
Revised
24 August 2020
24 August 2020
Accepted
24 August 2020
24 August 2020
Published
10 September 2020
10 September 2020
Abstract
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.
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