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A condition for the extinction of a branching process with an absorbing lower barrier

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Summary

A branching process with an absorbing lower barrier is considered. This is a Galton-Watson process with the condition that at any generation the number of individuals is greater than a lower barrier or it is equal to zero (i.e. all individuals in populations which are too small die and have no offspring). A necessary and sufficient condition is given for the process to become extinct with probability one. At the end of the paper there are three illustrating examples.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstraße 11/2, D-8520, Erlangen, Federal Republic of Germany

    H. -J. Schuh

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  1. H. -J. Schuh
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Now at the Division of Mathematics and Statistics, CSIRO, Canberra, A.C.T. 2601, Australia.

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Schuh, H.J. A condition for the extinction of a branching process with an absorbing lower barrier. J. Math. Biol. 3, 271–287 (1976). https://doi.org/10.1007/BF00275060

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  • DOI: https://doi.org/10.1007/BF00275060

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