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August 2011 Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials
Robert C. Griffiths, Dario Spanò
Bernoulli 17(3): 1095-1125 (August 2011). DOI: 10.3150/10-BEJ305

Abstract

Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre and Meixner are reviewed and their connection explored by adopting a probabilistic approach. Hahn and Meixner polynomials are interpreted as posterior mixtures of Jacobi and Laguerre polynomials, respectively. By using known properties of gamma point processes and related transformations, a new infinite-dimensional version of Jacobi polynomials is constructed with respect to the size-biased version of the Poisson–Dirichlet weight measure and to the law of the gamma point process from which it is derived.

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Robert C. Griffiths. Dario Spanò. "Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials." Bernoulli 17 (3) 1095 - 1125, August 2011. https://doi.org/10.3150/10-BEJ305

Information

Published: August 2011
First available in Project Euclid: 7 July 2011

zbMATH: 1247.33017
MathSciNet: MR2817619
Digital Object Identifier: 10.3150/10-BEJ305

Keywords: beta-Stacy , Dirichlet distribution , Hahn polynomials , Jacobi polynomials , Laguerre polynomials , Meixner polynomials , multivariate orthogonal polynomials , size-biased random discrete distributions

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

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Vol.17 • No. 3 • August 2011
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