Spine Changes of Measure and Branching Diffusions

Abstract

The main object of study in this thesis is branching Brownian motion, in which each particle moves like a Brownian motion and gives birth to new particles at some rate. In particular we are interested in where particles are located in this model at large times T : so, for a function f up to time T , we want to know how many particles have paths that look like f.Additive spine martingales are central to the study, and we also investigate some simple general properties of changes of measure related to such martingales.

Date of Award	1 Jun 2010
Original language	English
Awarding Institution	University of Bath
Supervisor	Simon Harris (Supervisor)