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

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.

Published in at http://dx.doi.org/10.3150/10-BEJ305 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (2)

• Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions
• Gibbs Sampling, Exponential Families and Orthogonal Polynomials

Cited by in corpus (7)

• An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection
• Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions
• Orthogonal polynomial kernels and canonical correlations for Dirichlet measures
• Hahn polynomials on polyhedra and quantum integrability
• Tight Frame with Hahn and Krawtchouk Polynomials of Several Variables
• Dual process in the two-parameter Poisson-Dirichlet diffusion
• The Rescaled Polya Urn and the Wright-Fisher process with mutation