Journal
JOURNAL OF APPLIED PROBABILITY
Volume 47, Issue 4, Pages 934-946Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1239/jap/1294170510
Keywords
Quasi-stationary distribution; total variation distance; stochastic logistic model
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Funding
- Schweizerischer Nationalfonds Projekt [20-107935/1]
- Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems
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Quasi-stationary distributions, as discussed in Darroch and Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In this paper, we give biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute.
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