Modelling quasistationarity in evanescent processes

Phil Pollett

Abstract: There are many stochastic systems which eventually "die out", yet appear to be stationary over any reasonable time scale. We will illustrate this phenomenon with reference to a variety of models arising in areas a diverse as ecology, epidemiology, chemical kinetics and telecommunications. We will explain how quasistationary distributions can be used to model the long-term behaviour of evanescent processes. We will look at questions concerning the existence of quasistationary distributions (something which is not always guaranteed in the infinite-state case) and computational techniques for evaluating them.

Acknowledgement: This worked was funded by the Australian Research Council.

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Last modified: 12th November 1998