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A result on the infinitely many neutral alleles diffusion model

Published online by Cambridge University Press:  14 July 2016

B. Schmuland
B. Schmuland*
Affiliation:
University of Alberta
*
∗Postal address: Department of Statistics and Applied Probability, University of Alberta, Edmonton, Alberta, Canada T6G 2G1.
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Abstract

The stationary version of the infinitely many neutral alleles diffusion model, as studied by Ethier and Kurtz, is constructed and analyzed using the theory of Dirichlet forms. We prove that the ‘boundary' of the state space is hit by the process iff θ < 1, where θ is the mutation parameter.

Keywords

INFINITE-DIMENSIONAL DIFFUSIONDIRICHLET FORMCAPACITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 253 - 267
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

Research supported by NSERC.

References

[1]Ethier, S. N. and Kurtz, T. G. (1981) The infinitely-many-neutral-alleles diffusion model. Adv. Appl. Prob. 13, 429–452.Google Scholar
[2]Ethier, S. N. and Kurtz, T. G. (1986) Markov Processes — Characterization and Convergence. Wiley-Interscience New York.Google Scholar
[3]Fukushima, M. (1980) Dirichlet Forms and Markov Processes. North-Holland, Amsterdam.Google Scholar
[4]Kingman, J. F. C. (1975) Random discrete distributions. J. R. Statist. Soc. B37, 1–22.Google Scholar
[5]Shiga, T. (1981) Diffusion processes in population genetics. J. Math. Kyoto Univ. 21(1), 133–151.Google Scholar
[6]Watterson, G. A. (1976) The stationary distribution of the infinitely many neutral alleles diffusion model. J. Appl. Prob. 13, 639–651.Google Scholar