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February, 2018 Coalescence on Supercritical Bellman-Harris Branching Processes
Krishna B. Athreya, Jyy-I Hong
Taiwanese J. Math. 22(1): 245-261 (February, 2018). DOI: 10.11650/tjm/8123

Abstract

We consider a continuous-time single-type age-dependent Bellman-Harris branching process $\{Z(t): t \geq 0\}$ with offspring distribution $\{p_j\}_{j \geq 0}$ and lifetime distribution $G$. Let $k \geq 2$ be a positive integer. If $Z(t) \geq k$, 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 $t \to \infty$.

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Krishna B. Athreya. Jyy-I Hong. "Coalescence on Supercritical Bellman-Harris Branching Processes." Taiwanese J. Math. 22 (1) 245 - 261, February, 2018. https://doi.org/10.11650/tjm/8123

Information

Received: 8 November 2016; Revised: 16 April 2017; Accepted: 23 May 2017; Published: February, 2018
First available in Project Euclid: 17 August 2017

zbMATH: 06965368
MathSciNet: MR3749363
Digital Object Identifier: 10.11650/tjm/8123

Subjects:
Primary: 60J80

Keywords: age-dependent , Bellman , branching processes , Coalescence , Harris , line of descent , supercritical

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

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Vol.22 • No. 1 • February, 2018
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