arXiv 0812.06572008-12math.PRmath.CA

Askey--Wilson polynomials, quadratic harnesses and martingales

Włodek Bryc, Jacek Wesołowski

备注：: Published in at http://dx.doi.org/10.1214/09-AOP503 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
发表信息：: Annals of Probability 2010, Vol. 38, No. 3, 1221-1262
DOI：: 10.1214/09-AOP503

英文摘要：

We use orthogonality measures of Askey--Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey--Wilson polynomials are orthogonal martingale polynomials for these processes.

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