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

Walker, Stephen G., Ruggiero, Matteo (2009) Countable representation for infinite-dimensional diffusions derived from the two parameter Poisson Dirichlet process. Electronic Communications in Probability, 14 . pp. 501-517. (doi:10.1214/ECP.v14-1508)

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## 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.

Item Type: Article 10.1214/ECP.v14-1508 Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics Stephen Walker 29 Jun 2011 13:37 UTC 28 May 2019 15:18 UTC https://kar.kent.ac.uk/id/eprint/23913 (The current URI for this page, for reference purposes)
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