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Free Quadratic Harness

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 the paper "Askey-Wilson polynomials, quadratic harnesses and martingales" by W. Bryc and J. Wesołowski using Askey--Wilson polynomials. Here we provide a self-contained construction of the free quadratic harness for all values of parameters.