Abstract: There are many stochastic systems which eventually "die out", yet appear to be stationary over any reasonable time scale. I will explore two approaches to modelling this behaviour. The first uses the idea of a limiting conditional (or quasi-stationary) distribution. I will explain how this distribution can be used model the long-term behaviour of these processes. In the second approach, I will describe a class of stochastic models (density-dependent Markov chains) for which there are identifiable deterministic analogues. I will delimit conditions under which a deterministic approximation is justified and then identify an approximating diffusion process that can be used to model fluctuations about the deterministic mean path.
Acknowledgement: This work is supported by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems
Last modified: 23rd September 2006