Countable representation for infinite dimensional diffusions derived from the two-parameter Poisson-Dirichlet process

Matteo Ruggiero (University of Pavia)
Stephen G. Walker (University of Kent)

Abstract


This paper provides a countable representation for a class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to the two-parameter Poisson-Dirichlet process. By means of Gibbs sampling procedures, we define a reversible Moran-type population process. The associated process of ranked relative frequencies of types is shown to converge in distribution to the two-parameter family of diffusions, which is stationary and ergodic with respect to the two-parameter Poisson-Dirichlet distribution. The construction provides interpretation for the limiting process in terms of individual dynamics.

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Pages: 501-517

Publication Date: November 26, 2009

DOI: 10.1214/ECP.v14-1508

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