Coalescence on Supercritical Bellman-Harris Branching Processes
Coalescence on Supercritical Bellman-Harris Branching Processes
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DOI：
10.11650/tjm/8123
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发表时间：
2018-02-01
影响因子：
0.4
通讯作者：
Hong, Jyy-I
中科院分区：
文献类型：
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作者：
Athreya, Krishna B.;Hong, Jyy-I
考虑连续时间单型年龄依赖Bellman-Harris分支过程{Z（t）：t >= 0}，其后代分布{p（j）}j >= 0，寿命分布G.设k >= 2为正整数。如果Z（t）>= k，我们通过简单随机抽样从t时存活的个体中挑选k个个体，不进行替换，并在时间上追溯他们的血统，直到他们第一次相遇。设D-k（t）为聚结时间（最近共同祖先的死亡时间），设X-k（t）为这k个随机选择的个体的最近共同祖先的代数。本文研究了D-k（t）和X-k（t）的分布及其在t ->无穷大时的极限分布
We consider a continuous-time single-type age-dependent Bellman-Harris branching process {Z(t) : t >= 0} with offspring distribution {p(j)}j >= 0 and lifetime distribution G. Let k >= 2 be a positive integer. If Z(t) >= k, 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 most recent common ancestor) and let X-k(t) be the generation number of the most recent common ancestor of these k random chosen individuals. In this paper, we study the distributions of D-k(t) and X-k(t) and their limit distributions as t -> infinity