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June 2013 Coalescence in subcritical Bellman-Harris age-dependent branching processes
Jyy-I Hong
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J. Appl. Probab. 50(2): 576-591 (June 2013). DOI: 10.1239/jap/1371648962

Abstract

We consider a continuous-time, single-type, age-dependent Bellman-Harris branching process. We investigate the limit distribution of the point process A(t)={at,i: 1≤ iZ(t)}, where at,i is the age of the ith individual alive at time t, 1≤ iZ(t), and Z(t) is the population size of individuals alive at time t. Also, if Z(t)k, k≥2, is a positive integer, we pick k individuals from those who are alive at time t by simple random sampling without replacement and trace their lines of descent backward in time until they meet for the first time. Let Dk(t) be the coalescence time (the death time of the last common ancestor) of these k random chosen individuals. We study the distribution of Dk(t) and its limit distribution as t→∞.

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Jyy-I Hong. "Coalescence in subcritical Bellman-Harris age-dependent branching processes." J. Appl. Probab. 50 (2) 576 - 591, June 2013. https://doi.org/10.1239/jap/1371648962

Information

Published: June 2013
First available in Project Euclid: 19 June 2013

zbMATH: 1270.60091
MathSciNet: MR3102501
Digital Object Identifier: 10.1239/jap/1371648962

Subjects:
Primary: 60J80
Secondary: 60G50

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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