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On a Theorem of Quine and Seneta for the Galton‐Watson Process With Immigration
Author(s) -
Pakes A. G.
Publication year - 1971
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1971.tb01256.x
Subject(s) - mathematics , limit (mathematics) , watson , limiting , quine , immigration , pure mathematics , calculus (dental) , mathematical analysis , philosophy , epistemology , law , computer science , mechanical engineering , medicine , dentistry , natural language processing , political science , engineering
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.