Trimmed sums and associated random variables in the q-domain of attraction of stable Laws

We introduce a concept of trimming in the context of q-probability and prove two limit theorems for absolutely trimmed q-sums of random variables in the strict domain of attraction of a non-Gaussian strictly stable law. For intermediately trimmed q-sums one always gets a Gaussian limit, whereas lightly trimmed q-sums converge to a limit which can be described by some generalizations of the classical Lévy construction of first kind of non-Gaussian stable laws. Furthermore, we carry over a stable limit theorem for associated random variables