Reinforced stochastic processes: theory and applications

Abstract

In this thesis, we study the asymptotic behaviour of the monkey walk, a stochastic process with reinforcement. The monkey walk behaves as a Markovian process except at some random times when it jumps to positions it has already visited. The main difficulty in the study of the monkey walk is the non-Markovianity of the process. The monkey walk was introduced by physicists to model animal foraging behaviour.

We obtain two results: a Cental Limit Theorem (Chapter 3) and a Large Deviations Principle (Chapter 2) for the position of the walker. In Chapter 4, we indicate open questions and suggest possible directions for future research on the monkey walk.

Date of Award	26 Apr 2023
Original language	English
Awarding Institution	University of Bath
Supervisor	Cecile Mailler (Supervisor) & Matt Roberts (Supervisor)