Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials
Probability
2007-11-27 v1 Mathematical Physics
math.MP
Abstract
We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-commutation relation. This implies that quadratic harnesses are essentially determined uniquely by five numerical constants. Explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest.
Cite
@article{arxiv.math/0504194,
title = {Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials},
author = {Wlodzimierz Bryc and Wojciech Matysiak and Jacek Wesolowski},
journal= {arXiv preprint arXiv:math/0504194},
year = {2007}
}