Author:
Ethier S. N.,Kurtz Thomas G.
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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
14 articles.
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