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

DOI10.3150/10-BEJ305zbMath1247.33017arXiv0809.1431OpenAlexW3105771126MaRDI QIDQ638771

Robert C. Griffiths, Dario Spanò

Publication date: 14 September 2011

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.1431

zbMATH Keywords

Dirichlet distributionJacobi, Laguerre, Hahn and Meixner polynomialsMultivariable orthogonal polynomialsreview and extensionssize-biased distributions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items

An algebraic interpretation of the multivariate \(q\)-Krawtchouk polynomials, Eigenfunctions and the Dirichlet Problem for the Classical Kimura Diffusion Operator, Moment-based density estimation of confidential micro-data: a computational statistics approach, Orthogonal polynomial kernels and canonical correlations for Dirichlet measures, Numerical approximation of high-dimensional Fokker-Planck equations with polynomial coefficients, Hahn polynomials on polyhedra and quantum integrability, Hahn, Jacobi, and Krawtchouk polynomials of several variables

Cites Work

• Jacobi polynomials in Bernstein form
• Gibbs sampling, exponential families and orthogonal polynomials
• Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions
• On the distribution of allele frequencies in a diffusion model
• Beta-stacy processes and a generalization of the Pólya-Urn scheme
• Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle
• Tailfree and neutral random probabilities and their posterior distributions
• Exchangeable and partially exchangeable random partitions
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• On the Bernstein--Bézier form of Jacobi polynomials on a simplex
• Diffusion processes and coalescent trees
• Random discrete distributions invariant under size-biased permutation
• On Some Expansions in Laguerre Polynomials
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item