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September 2016 Coalescence on critical and subcritical multitype branching processes
Jyy-I Hong
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J. Appl. Probab. 53(3): 802-817 (September 2016).

Abstract

Consider a d-type (d<∞) Galton–Watson branching process, conditioned on the event that there are at least k≥2 individuals in the nth generation, pick k individuals at random from the nth generation and trace their lines of descent backward in time till they meet. In this paper, the limit behaviors of the distributions of the generation number of the most recent common ancestor of any k chosen individuals and of the whole population are studied for both critical and subcritical cases. Also, we investigate the limit distribution of the joint distribution of the generation number and their types.

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Jyy-I Hong. "Coalescence on critical and subcritical multitype branching processes." J. Appl. Probab. 53 (3) 802 - 817, September 2016.

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Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60113
MathSciNet: MR3570095

Subjects:
Primary: 60J80
Secondary: 60F10

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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