Quadratic Harnesses, q-commutations, and orthogonal martingale polynomials
概率论
2007-11-27 v1 数学物理
math.MP
摘要
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.
引用
@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}
}