Taboo extinction, sojourn times, and asymptotic growth for the Markovian birth and death process

1 June 1972

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 9 (3) , 486-506
https://doi.org/10.2307/3212321

Abstract

A well-known result in the theory of branching processes provides an asymptotic expression for the population size (valid for large times) in terms of a single random variable, multiplied by a deterministic exponential growth factor. In the present paper this is generalized to a class of size-dependent population models. The work is based on the series of sojourn times. An essential tool is the use of probabilities conditional upon non-extinction (taboo probabilities).

Keywords

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