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2010 Multidimensional $q$-Normal and Related Distributions - Markov Case
Pawel Szablowski
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Electron. J. Probab. 15: 1296-1318 (2010). DOI: 10.1214/EJP.v15-796

Abstract

We define and study distributions in $\mathbb{R}^d$ that we call $q$-Normal. For $q=1$ they are really multidimensional Normal, for $q$ in $(-1,1)$ they have densities, compact support and many properties that resemble properties of ordinary multidimensional Normal distribution. We also consider some generalizations of these distributions and indicate close relationship of these distributions to Askey-Wilson weight function i.e. weight with respect to which Askey-Wilson polynomials are orthogonal and prove some properties of this weight function. In particular we prove a generalization of Poisson-Mehler expansion formula

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Pawel Szablowski. "Multidimensional $q$-Normal and Related Distributions - Markov Case." Electron. J. Probab. 15 1296 - 1318, 2010. https://doi.org/10.1214/EJP.v15-796

Information

Accepted: 14 August 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1222.62061
MathSciNet: MR2678392
Digital Object Identifier: 10.1214/EJP.v15-796

Subjects:
Primary: 62H10
Secondary: 60E05, 60E99, 62E10

JOURNAL ARTICLE
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Vol.15 • 2010
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