The Annals of Probability

Askey–Wilson polynomials, quadratic harnesses and martingales

Włodek Bryc and Jacek Wesołowski

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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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Ann. Probab., Volume 38, Number 3 (2010), 1221-1262.

First available in Project Euclid: 2 June 2010

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Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 46L53: Noncommutative probability and statistics

Quadratic conditional variances harnesses orthogonal martingale polynomials hypergeometric orthogonal polynomials


Bryc, Włodek; Wesołowski, Jacek. Askey–Wilson polynomials, quadratic harnesses and martingales. Ann. Probab. 38 (2010), no. 3, 1221--1262. doi:10.1214/09-AOP503.

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