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Further approaches to computing fundamental characteristics of birth-death processes

  • Frank Ball (a1) and Valeri T. Stefanov (a2)


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.


Corresponding author

Postal address: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK. Email address:
∗∗ Postal address: Department of Mathematics and Statistics, The University of Western Australia, Crawley 6009, WA, Australia.


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