The infinitely-many-neutral-alleles diffusion model
- 1 September 1981
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 13 (3), 429-452
- https://doi.org/10.2307/1426779
Abstract
A diffusion processX(·) in the infinite-dimensional ordered simplex is characterized in terms of the generator defined on an appropriate domain. It is shown thatX(·) is the limit in distribution of several sequences of discrete stochastic models of the infinitely-many-neutral-alleles type. It is further shown thatX(·) has a unique stationary distribution and is reversible and ergodic. Kingman's limit theorem for the descending order statistics of the symmetric Dirichlet distribution is obtained as a corollary.Keywords
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