Perturbations of Markov Chains

Abstract

This thesis is concerned with studying the hitting time of an absorbing state on Markov chain models that have a countable state space. For many models it is challenging to study the hitting time directly; I present a perturbative approach that allows one to uniformly bound the difference between the hitting time moment generating functions of two Markov chains in a neighbourhood of the origin. I demonstrate how this result can be applied to both discrete and continuous time Markov chains.

The motivation for this work came from the field of biology, namely DNA damage and repair. Biophysicists have highlighted that the repair process can lead to Double Strand Breaks; due to the serious nature of such an eventuality it is important to understand the hitting time of this event. There is a phase transition in the model that I consider. In the regime of parameters where the process reaches quasi-stationarity before being absorbed I am able to apply my perturbative technique in order to further understand this hitting time.