The bi-Poisson process: a quadratic harness

Details The bi-Poisson process: a quadratic harness The bi-Poisson process: a quadratic harness

2005-10-11

arxiv.org/abs/math/0510208v2

Annals of Probability 2008, Vol. 36, No. 2, 623-646

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/009117907000000268 the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117907000000268

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.

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