Journal of Applied Probability

Coalescence in subcritical Bellman-Harris age-dependent branching processes

Jyy-I Hong

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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

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

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Branching process coalescence subcritical Bellman Harris age dependent line of descent


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.

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