Journal of Applied Probability

Coalescence in subcritical Bellman-Harris age-dependent branching processes

Jyy-I Hong

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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→∞.

Article information

Source
J. Appl. Probab., Volume 50, Number 2 (2013), 576-591.

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648962

Digital Object Identifier
doi:10.1239/jap/1371648962

Mathematical Reviews number (MathSciNet)
MR3102501

Zentralblatt MATH identifier
1270.60091

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G50: Sums of independent random variables; random walks

Keywords
Branching process coalescence subcritical Bellman Harris age dependent line of descent

Citation

Hong, Jyy-I. Coalescence in subcritical Bellman-Harris age-dependent branching processes. J. Appl. Probab. 50 (2013), no. 2, 576--591. doi:10.1239/jap/1371648962. https://projecteuclid.org/euclid.jap/1371648962


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References

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