Włodzimierz Bryc, Wojciech Matysiak, Jacek Wesołowski
Published 2005-10-11, updated 2008-04-21Version 2
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.
Comments: Published in at http://dx.doi.org/10.1214/009117907000000268 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2008, Vol. 36, No. 2, 623-646
Bi-Poisson process
On integrability of quadratic harnesses
Probabilistic implications of symmetries of q-Hermite and Al-Salam-Chihara polynomials
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