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≤ i≤ Z(t)}, where at,i is the age of the ith individual alive at time t, 1≤ i≤ Z(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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