Coalescence in Subcritical Bellman-Harris Age-Dependent Branching Processes
2013 ◽
Vol 50
(02)
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pp. 576-591
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Keyword(s):
We consider a continuous-time, single-type, age-dependent Bellman-Harris branching process. We investigate the limit distribution of the point process A(t)={a t,i : 1≤ i≤ Z(t)}, where a t,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 D k(t) be the coalescence time (the death time of the last common ancestor) of these k random chosen individuals. We study the distribution of D k(t) and its limit distribution as t→∞.
Keyword(s):
2012 ◽
Vol 49
(03)
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pp. 627-638
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2012 ◽
Vol 49
(3)
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pp. 627-638
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1969 ◽
Vol 6
(01)
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pp. 195-200
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1971 ◽
Vol 8
(03)
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pp. 589-598
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