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

Walker, S.G. and Ruggiero, M. (2009) Countable representation for infinite-dimensional diffusions derived from the two parameter Poisson Dirichlet process. Electronic Communications in Probability, 14 . pp. 501-517. (Full text available)

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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
Subjects: Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Stephen Walker
Date Deposited: 29 Jun 2011 13:37
Last Modified: 05 Dec 2011 15:22
Resource URI: http://kar.kent.ac.uk/id/eprint/23913 (The current URI for this page, for reference purposes)
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