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Total variation approximation for quasi-stationary distributions


Barbour, A D; Pollett, P K (2010). Total variation approximation for quasi-stationary distributions. Journal of Applied Probability, 47(4):934-946.

Abstract

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.

Abstract

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Physical Sciences > General Mathematics
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Language:English
Date:2010
Deposited On:27 Dec 2017 15:11
Last Modified:31 Jul 2020 01:33
Publisher:Applied Probability Trust
ISSN:0021-9002
Funders:Schweizerischer Nationalfonds
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1017/S0021900200007270

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