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April 2008 Distributions of linear functionals of two parameter Poisson–Dirichlet random measures
Lancelot F. James, Antonio Lijoi, Igor Prünster
Ann. Appl. Probab. 18(2): 521-551 (April 2008). DOI: 10.1214/07-AAP462

Abstract

The present paper provides exact expressions for the probability distributions of linear functionals of the two-parameter Poisson–Dirichlet process PD(α, θ). We obtain distributional results yielding exact forms for density functions of these functionals. Moreover, several interesting integral identities are obtained by exploiting a correspondence between the mean of a Poisson–Dirichlet process and the mean of a suitable Dirichlet process. Finally, some distributional characterizations in terms of mixture representations are proved. The usefulness of the results contained in the paper is demonstrated by means of some illustrative examples. Indeed, our formulae are relevant to occupation time phenomena connected with Brownian motion and more general Bessel processes, as well as to models arising in Bayesian nonparametric statistics.

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Lancelot F. James. Antonio Lijoi. Igor Prünster. "Distributions of linear functionals of two parameter Poisson–Dirichlet random measures." Ann. Appl. Probab. 18 (2) 521 - 551, April 2008. https://doi.org/10.1214/07-AAP462

Information

Published: April 2008
First available in Project Euclid: 20 March 2008

zbMATH: 1138.60040
MathSciNet: MR2398765
Digital Object Identifier: 10.1214/07-AAP462

Subjects:
Primary: 60G57
Secondary: 60E07, 60G51, 62F15

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 2 • April 2008
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