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Further approaches to computing fundamental characteristics of birth-death processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Frank Ball  and
Valeri T. Stefanov
Frank Ball*
Affiliation:
University of Nottingham
Valeri T. Stefanov*
Affiliation:
The University of Western Australia
*
∗ Postal address: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK. Email address: fgb@maths.nott.ac.uk
∗∗ Postal address: Department of Mathematics and Statistics, The University of Western Australia, Crawley 6009, WA, Australia.
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Abstract

General and unifying approaches are discussed for computing fundamental characteristics of both continuous-time and discrete-time birth-death processes. In particular, an exponential family framework is used to derive explicit expressions, in terms of continued fractions, for joint generating functions of first-passage times and a whole collection of associated random quantities, and a random sum representation is used to obtain formulae for means, variances and covariances of stopped reward functions defined on a birth-death process.

Keywords

Birth-death processstopping timeexponential family

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60J22: Computational methods in Markov chains
Secondary: 92D30: Epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 995 - 1005
Copyright
Copyright © by the Applied Probability Trust 2001 

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