Un théorème limite central dans un hypergroupe bidimensionnel. (A central limit theorem on a two-dimensional hypergroup)
type: Item
instance of: scholarly article
title: Un théorème limite central dans un hypergroupe bidimensionnel. (A central limit theorem on a two-dimensional hypergroup)
zbMATH Open document ID: 0748.60025
author: Mostafa Bouhaik
author: Léonard Gallardo
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1992-09-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77424
review text: The Mehler-Heine formula of \textit{M. Bouhaik} and \textit{L. Gallardo} [Indag. Math., New Ser. 2, No. 1, 9-18 (1991; Zbl 0727.33003)] is used to derive central limit theorems for a large class of Markov chains on the two-dimensional hypergroups \(\mathbb{N}_ 0^ 2\) which are associated with the linearization formulas of the disk polynomials, i.e. Jacobi polynomials in two variables. Moreover, a strong law of large numbers for Markov chains on these hypergroups is given.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 43A62
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 57275
zbMATH Keywords: Mehler-Heine formula
zbMATH Keywords: Markov chains on the two-dimensional hypergroups
zbMATH Keywords: Jacobi polynomials
reviewed by: Michael Voit
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 57275