Total variation approximation for quasi-equilibrium distributions

Details Total variation approximation for quasi-equilibrium distributions Total variation approximation for quasi-equilibrium distributions

2010-04-13

arxiv.org/abs/1004.2252v1

Mathematics

Probability

16 pages

Scientific paper

Quasi-stationary distributions, as discussed by Darroch & 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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