The bi-Poisson process: a quadratic harness
Probability
2009-09-29 v2
Abstract
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.
Cite
@article{arxiv.math/0510208,
title = {The bi-Poisson process: a quadratic harness},
author = {Włodzimierz Bryc and Wojciech Matysiak and Jacek Wesołowski},
journal= {arXiv preprint arXiv:math/0510208},
year = {2009}
}
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)