Total variation approximation for quasi-equilibrium distributions, II

AD Barbour; PK Pollett

Journal article

Total variation approximation for quasi-equilibrium distributions, II

AD Barbour, PK Pollett

Stochastic Processes and their Applications | ELSEVIER SCIENCE BV | Published : 2012

DOI: 10.1016/j.spa.2012.07.004

Abstract

Quasi-stationary distributions have been used in biology to describe the steady state behaviour of Markovian population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. However, they have substantial drawbacks; a Markov process may not possess any, or may have several, and their probabilities can be very difficult to determine. Here, we consider conditions under which an apparent stochastic equilibrium distribution can be identified and computed, irrespective of whether a quasi-stationary distribution exists, or is unique; we call it a quasi-equilibrium distribution. The results are applied to multi-dimension..

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University of Melbourne Researchers

Andrew Barbour Author

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Grants

Awarded by Australian Research Council

Funding Acknowledgements

[ "ADB wishes to thank the Institute for Mathematical Sciences at the National University of Singapore, the Department of Mathematics and Statistics at the University of Melbourne, the School of Mathematical Sciences at Monash University and the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, for their hospitality and financial support while part of this work was accomplished. PKP was supported in part by the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems.", "The first author's work was supported in part by Australian Research Council Grants Nos DP120102728 and DP120102398." ]