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    Richard, Mathieu 2014. Splitting trees with neutral mutations at birth. Stochastic Processes and their Applications, Vol. 124, Issue. 10, p. 3206.


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    Pakes, Anthony G. 2003. Stochastic Processes: Modelling and Simulation.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 46, Issue 1
  • February 1989, pp. 146-169

An infinite alleles version of the Markov branching process

  • Anthony G. Pakes (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700030445
  • Published online: 01 April 2009
Abstract
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2]K. B. Athreya and P. E. Ney , Branching processes (Springer-Verlag, Berlin, 1972).

[5]S. Karlin and J. McGregor , ‘On the spectral representation of branching processes with mean one’, J. Math. Anal. Appl. 21 (1968), 485495.

[6]T. Lindvall , ‘On coupling of discrete renewal processes’, Z. Wahrsch. Verw. Gebiete 48 (1979), 5770.

[8]A. G. Pakes , ‘The age of a Markov process’, Stochastic Process Appl. 8 (1979), 277303.

[9]V. M. Zolotarev , ‘More exact statements of several theorems in the theory of branching processes’, Theor. Probab. Appl. 2 (1957), 245253.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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