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Computable Bounds for the Decay Parameter of a Birth–Death Process

Part of: Markov processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

David Sirl ,
Hanjun Zhang  and
Phil Pollett
David Sirl*
Affiliation:
The University of Queensland
Hanjun Zhang*
Affiliation:
The University of Queensland
Phil Pollett*
Affiliation:
The University of Queensland
*
∗ Postal address: Department of Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia.
∗ Postal address: Department of Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia.
∗ Postal address: Department of Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia.
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Abstract

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We present bounds on the decay parameter for absorbing birth–death processes adapted from results of Chen (2000), (2001). We address numerical issues associated with computing these bounds, and assess their accuracy for several models, including the stochastic logistic model, for which estimates of the decay parameter have been obtained previously by Nåsell (2001).

Keywords

Approximation; exponential ergodicityquasi-stationary distribution

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 65C20: Models, numerical methods
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 476 - 491
Copyright
Copyright © Applied Probability Trust 2007 

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