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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) (KAR id:23913)

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
DOI/Identification number: 10.1214/ECP.v14-1508
Subjects: Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Stephen Walker
Date Deposited: 29 Jun 2011 13:37 UTC
Last Modified: 16 Nov 2021 10:02 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/23913 (The current URI for this page, for reference purposes)

University of Kent Author Information

Walker, Stephen G..

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