Askey--Wilson polynomials, quadratic harnesses and martingales
arXiv:0812.0657 · doi:10.1214/09-AOP503
Abstract
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)
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Cited by in corpus (26)
- Markov processes related to the stationary measure for the open KPZ equation
- On the structure and probabilistic interpretation of Askey-Wilson densities and polynomials with complex parameters
- Expansions of one density via polynomials orthogonal with respect to the other
- Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
- Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
- From the asymmetric simple exclusion processes to the stationary measures of the KPZ fixed point on an interval
- Befriending Askey-Wilson polynomials
- Stationary measures of the KPZ equation on an interval from Enaud-Derrida's matrix product ansatz representation
- Nevanlinna Theory of the Wilson Divided-difference Operator
- Hahn polynomials and the Burnside process
- Tridiagonal representations of the q-oscillator algebra and Askey-Wilson polynomials
- Approximating the stationary distribution of the ASEP with open boundaries
- A few remarks on quadratic harnesses
- Askey-Wilson signed measures and open ASEP in the shock region
- On the continuous dual Hahn process
- Semigroups of distributions with linear Jacobi parameters
- Markov processes, polynomial martingales and orthogonal polynomials
- Fluctuations of random Motzkin paths II
- On the families of polynomials forming a part of the Askey--Wilson scheme and their probabilistic applications
- Wilson's 6-j laws and stitched Markov processes
- Free Quadratic Harness
- Stationary measure for six-vertex model on a strip
- Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths
- Bridges of quadratic harnesses
- Limits of open ASEP stationary measures near a boundary
- On second order q-difference equations for high-order Sobolev-type q-Hermite orthogonal polynomials