A few remarks on quadratic harnesses

Abstract

We analyse and partially solve system of recurrences that can be derived from the properties of orthogonal martingale polynomials that characterize quadratic harnesses (QHs). We also specify conditions for the existence of moments of one dimensional distributions for large classes of QHs that are also Markov processes complementing earlier results.

Keywords::

• system of difference equations
• orthogonal polynomials
• q-series
• three-term recurrence

MSC (2010) Classification::

• Primary 39A10, 39A13
• Secondary 33D45, 60G44

Acknowledgement

The author would like to thank the unknown referee for pointing out numerous mistakes, inaccu-racies and misprints of the first version of the paper.