Bernoulli

  • Bernoulli
  • Volume 17, Number 3 (2011), 1095-1125.

Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials

Robert C. Griffiths and Dario Spanò

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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.

Article information

Source
Bernoulli, Volume 17, Number 3 (2011), 1095-1125.

Dates
First available in Project Euclid: 7 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1310042858

Digital Object Identifier
doi:10.3150/10-BEJ305

Mathematical Reviews number (MathSciNet)
MR2817619

Zentralblatt MATH identifier
1247.33017

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

Citation

Griffiths, Robert C.; Spanò, Dario. Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials. Bernoulli 17 (2011), no. 3, 1095--1125. doi:10.3150/10-BEJ305. https://projecteuclid.org/euclid.bj/1310042858


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