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

1971; Wiley; Volume: 13; Issue: 3 Linguagem: Inglês

10.1111/j.1467-842x.1971.tb01256.x

0004-9581

Anthony G. Pakes,

Diffusion and Search Dynamics

Summary 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.