Free quadratic harness

Abstract

Free quadratic harness is a Markov process from the class of quadratic harnesses, i.e. processes with linear regressions and quadratic conditional variances. The process has recently been constructed for a restricted range of parameters in Bryc et al. (2010) [7] using Askey-Wilson polynomials. Here we provide a self-contained construction of the free quadratic harness for all values of the parameters.Quadratic conditional variances Harnesses Orthogonal martingale polynomials Free Lévy processes Hypergeometric orthogonal polynomials