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An infinite alleles version of the Markov branching process

Part of: Markov processes

Published online by Cambridge University Press:  09 April 2009

Anthony G. Pakes
Anthony G. Pakes
Affiliation:
Department of MathematicsUniversity of Western Australia Nedlands, W. A. 6009, Australia
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Abstract

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Individuals in a population which grows according to the rules defining the Markov branching process can mutate into novel allelic forms. We obtain some results about the time of the last mutation and the limiting frequency spectrum. In the present context these results refine certain results obtained in the discrete time case and they answer some conjectures still unresolved for the discrete time case.

Keywords

Markov branching processinfinite alleles mode.

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 146 - 169
Copyright
Copyright © Australian Mathematical Society 1989

References

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