The infinitely-many-neutral-alleles diffusion model
- 1 March 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 13 (03), 429-452
- https://doi.org/10.1017/s0001867800036211
Abstract
A diffusion process X(·) in the infinite-dimensional ordered simplex is characterized in terms of the generator defined on an appropriate domain. It is shown that X(·) is the limit in distribution of several sequences of discrete stochastic models of the infinitely-many-neutral-alleles type. It is further shown that X(·) 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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