Degree Type

Dissertation

Date of Award

2011

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Krishna B. Athreya

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).

DOI

https://doi.org/10.31274/etd-180810-1744

Copyright Owner

Jyy-i Joy Hong

Language

en

Date Available

2012-04-06

File Format

application/pdf

File Size

151 pages

Included in

Mathematics Commons

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