An empirical study of some branching processes with upper barrier

Authors

Alejandro Aguilar, University of Texas-Pan American

Date of Award

8-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. George Yanev

Second Advisor

Dr. Santanu Chakraborty

Third Advisor

Dr. Xiaohui Wang

Abstract

We consider discrete time branching processes with a reflecting upper barrier. The processes differ in their offspring distributions being either binary splitting or binomial one. Two important factors for the behavior of the processes characteristics are studied as follows: time to extinction and total progeny up to the n th generation. More specifically, we investigate the distribution and expected value of the time to extinction as well as the probability mass functions of the total progeny. The tools used are basic results for a finite state Markov chain.

Comments

Copyright 2014 Alejandro Aguilar. All Rights Reserved.

https://www.proquest.com/dissertations-theses/empirical-study-some-branching-processes-with/docview/1629825702/se-2

Granting Institution

University of Texas-Pan American