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Conditional Limit Laws and Inference for Generation Sizes of Branching Processes

P. E. Ney and A. N. Vidyashankar

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Abstract

Let {Zn:n0} 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 RnZn+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.

Chapter information

Source
Stewart N. Ethier, Jin Feng and Richard H. Stockbridge, eds., Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 17-30

Dates
First available in Project Euclid: 28 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1233152932

Digital Object Identifier
doi:10.1214/074921708000000273

Mathematical Reviews number (MathSciNet)
MR2574221

Zentralblatt MATH identifier
1167.60349

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Ney, P. E.; Vidyashankar, A. N. Conditional Limit Laws and Inference for Generation Sizes of Branching Processes. Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz, 17--30, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000273. https://projecteuclid.org/euclid.imsc/1233152932


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