A few remarks on quadratic harnesses
Pawe{\l} J. Szab{\l}owski
TL;DR
This paper investigates quadratic harnesses by analyzing recurrence systems from martingale orthogonal polynomials, providing conditions for the existence of moments in these Markov processes and extending previous results.
Contribution
It offers a partial solution to recurrence systems and specifies moment existence conditions for a broad class of quadratic harnesses, enhancing understanding of their properties.
Findings
Derived conditions for moments in quadratic harnesses
Analyzed recurrence systems from martingale polynomials
Extended previous results on quadratic harnesses
Abstract
We analyze and partially solve system of recurrences that can be derived from the properties of martingale orthogonal polynomials that characterize quadratic harnesses (QH). We also specify conditions for the existence of moments of one dimensional distribution for large classes of quadratic harnesses that are also Markov processes complementing earlier results.
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