On a Theorem of Quine and Seneta for the Galton-Watson Process With Immigration

Recently a limit theorem has been obtained for the limiting-stationary distribution of a process in which individuals reproduce as in a subcritical Galton-Watson process and are subject to an independent immigration component at each generation. This paper provides a different proof of this theorem, and under slightly weaker conditions. A similar approach is used to obtain a limit form of Taglom's theorem for the ordinary subcritical Galton-Watson process.