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Coalescence on critical and subcritical multitype branching processes

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  24 October 2016

Jyy-I Hong
Jyy-I Hong*
Affiliation:
National Sun Yat-sen University
*
* Postal address: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan. Email address: hongjyyi@gmail.com
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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.

Keywords

Branching processcoalescencecriticalsubcriticalmultitypeline of descent

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 802 - 817
Copyright
Copyright © Applied Probability Trust 2016 

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References

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