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

作者：Griffiths Robert C^*; Spano Dario

来源：Bernoulli, 2011, 17(3): 1095-1125.

DOI：10.3150/10-BEJ305

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

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.

• 出版日期2011-8