Conditional Limit Laws and Inference for Generation Sizes of Branching Processes
P. E. Ney, A. N. Vidyashankar
Abstract
Let {Zn:n≥0} denote a single type supercritical branching process initiated by a single ancestor. This paper studies the asymptotic behavior of the history of generation sizes conditioned on different notions of information about the “current” population size. A “suppression property” under the large deviation conditioning, namely that Rn≡Zn+1/Zn>a, is observed. Furthermore, under a more refined conditioning, the asymptotic aposteriori distribution of the original offspring distribution is developed. Implications of our results to conditional consistency property of age is discussed.
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1233152932
Digital Object Identifier: doi:10.1214/074921708000000273
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