This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam–Chihara polynomials and a relation between these polynomials for different values of parameters.
"The bi-Poisson process: A quadratic harness." Ann. Probab. 36 (2) 623 - 646, March 2008. https://doi.org/10.1214/009117907000000268