Central limit theorems for random walks on \({\mathbb{N}}_ 0\) that are associated with orthogonal polynomials

DOI10.1016/0047-259X(90)90041-FzbMath0722.60021MaRDI QIDQ756243

Michael Voit

Publication date: 1990

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

rate of convergenceorthogonal polynomialsfinitely generated semigroupspolynomial hypergroupsCentral limit theoremsinfinite distance-transitive graphs

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Convergence of probability measures (60B10)

Related Items (21)

Prediction of weakly stationary sequences on polynomial hypergroups ⋮ Positivity of Gibbs states on distance-regular graphs ⋮ Limit theorems for isotropic random walks on triangle buildings ⋮ Rate of escape and central limit theorem for the supercritical Lamperti problem ⋮ Compact groups having almost discrete orbit hypergroups ⋮ A law of the iterated logarithm for martingales ⋮ Representations of double coset hypergroups and induced representations ⋮ Dispersion and limit theorems for random walks associated with hypergeometric functions of type \(BC\) ⋮ CONTINUOUS ASSOCIATION SCHEMES AND HYPERGROUPS ⋮ Pseudoisotropic random walks on free groups and semigroups ⋮ On the Fourier transformation of positive, positive definite measures on commutative hypergroups, and dual convolution structures ⋮ The spectral connection matrix for classical orthogonal polynomials of a single parameter ⋮ Duals of subhypergroups and quotients of commutative hypergroups ⋮ Moment functions and laws of large numbers on hypergroups ⋮ Strong laws of large numbers for random walks associated with a class of one-dimensional convolution structures ⋮ On the rate of convergence of the laws of Markov chains associated with orthogonal polynomials ⋮ A formula of Hilb's type for orthogonal polynomials ⋮ A product formula for orthogonal polynomials associated with infinite distance-transitive graphs ⋮ A law of the iterated logarithm for Markov chains on \(\mathbb{N}_ 0\) associated with orthogonal polynomials ⋮ A multidimensional central limit theorem for random walks on hypergroups ⋮ Invariance principles for random walks on hypergroups on \(\mathbb{R}_ +\) and \(\mathbb{N}\)

Cites Work

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• The rate of escape for anisotropic random walks in a tree
• Laws of large numbers for hypergroups on \({\mathbb{R}}_+\)
• Limit theorems for random walks on discrete semigroups related to nonhomogeneous trees and Chebyshev polynomials
• Infinite distance transitive graphs of finite valency
• Spaces with an abstract convolution of measures
• Marches aléatoires sur les groupes de Lie
• The central limit theorem for Chébli-Trimèche hypergroups
• Laws of large numbers for polynomial hypergroups and some applications
• Comportement asymptotique des marches aleatoires associees aux polynomes de Gegenbauer et applications
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Isotropic random walks in a tree
• Central limit theorems for a class of polynomial hypergroups

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