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 Electronic Journal of Probability > Vol. 15(2010) > Paper 40 open journal systems 


Multidimensional q-Normal and related distributions - Markov case

Paweł Jerzy Szabłowski, Warsaw University of Technology


Abstract
We define and study distributions in Rd that we call q-Normal. For q=1 they are really multidimensional Normal, for q∈(-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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Pages: 1296-1318

Published on: August 14, 2010
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Electronic Journal of Probability. ISSN: 1083-6489