Coalescence in Bellman-Harris and multi-type branching processes

Date
2011-01-01
Authors
Hong, Jyy-i
Major Professor
Advisor
Krishna B. Athreya
Committee Member
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Mathematics
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Mathematics
Abstract

For branching processes, there are many well-known limit theorems

regarding the evolution of the population in the future time. In

this dissertation, we investigate the other direction of the

evolution, that is, the past of the processes. We pick some

individuals at random by simple random sampling without replacement

and trace their lines of descent backward in time until they meet.

We study the coalescence problem of the discrete-time multi-type

Galton-Watson branching process and both the continuous-time

single-type and multi-type Bellman-Harris branching processes

including the generation number, the death time (in the

continuous-time processes)

and the type (in the multi-type processes) of the last common ancestor

( also called the most recent common ancestor) of the randomly

chosen individuals for the different cases (supercritical, critical, subcritical and explosive).

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