  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.
