Askey–Wilson polynomials, quadratic harnesses and martingales
Copyright policy )Askey–Wilson polynomials, quadratic harnesses and martingales
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.
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)
- University of Cincinnati United States
- University System of Ohio United States
- Warsaw University of Technology Poland
hypergeometric orthogonal polynomials, harnesses, Probability (math.PR), Noncommutative probability and statistics, orthogonal martingale polynomials, orthogonal martingale polynomial, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), 60J25, Mathematics - Classical Analysis and ODEs, hypergeometric orthogonal polynomial, Quadratic conditional variances, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Continuous-time Markov processes on general state spaces, quadratic conditional variance, 46L53, harness, Mathematics - Probability
hypergeometric orthogonal polynomials, harnesses, Probability (math.PR), Noncommutative probability and statistics, orthogonal martingale polynomials, orthogonal martingale polynomial, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), 60J25, Mathematics - Classical Analysis and ODEs, hypergeometric orthogonal polynomial, Quadratic conditional variances, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Continuous-time Markov processes on general state spaces, quadratic conditional variance, 46L53, harness, Mathematics - Probability
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