q-Stieltjes classes for some families of q-distributions

TL;DR

This paper introduces the concept of q-moment determinacy and indeterminacy, defining q-analogues of Stieltjes classes, and constructs such classes for q-distributions with indeterminate moments.

Contribution

It proposes a new framework for q-moment problems and constructs q-Stieltjes classes for families of q-distributions with indeterminate moments.

Findings

Defined q-moment determinacy and indeterminacy.

Established conditions for q-moment determinacy.

Constructed q-Stieltjes classes for specific q-distributions.

Abstract

The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly an infinite family of probability densities with the same sequence of moments. In this paper, the notion of $q$-moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either $q$-moment determinate or indeterminate in terms of its $q$-density have been obtained. Also, a $q$-analogue of Stieltjes classes is defined for $q$-distributions and $q$-Stieltjes classes have been constructed for a family of $q$-densities of $q$-moment indeterminate distributions.