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2009 Countable representation for infinite dimensional diffusions derived from the two-parameter Poisson-Dirichlet process
Matteo Ruggiero, Stephen Walker
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Electron. Commun. Probab. 14: 501-517 (2009). DOI: 10.1214/ECP.v14-1508

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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Matteo Ruggiero. Stephen Walker. "Countable representation for infinite dimensional diffusions derived from the two-parameter Poisson-Dirichlet process." Electron. Commun. Probab. 14 501 - 517, 2009. https://doi.org/10.1214/ECP.v14-1508

Information

Accepted: 26 November 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60103
MathSciNet: MR2564485
Digital Object Identifier: 10.1214/ECP.v14-1508

Subjects:
Primary: 60G57
Secondary: 60J60, 92D25

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