Generating functions in branching processes and birth and death processes

Abstract

"If I have seen further, it is by standing upon the shoulders of giants" -Sir Isaac Newton Birth and death processes and branching processes are areas of stochastic processes that can be applied to a multitude of elds and disciplines, such as biology, economics and engineering. In general, the analysis of distributions and moments of these processes are di cult to obtain in explicit form. The use of generating functions makes computation much easier. The dissertation looks at the theory, application and innovation of using generating functions in the analysis of branching and birth and death processes.