Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences

This note contains a Chover-type Law of the k-Iterated Logarithm for weighted sums of strong mixing sequences of random variables with a distribution in the domain of a stable law. We show that the upper part of the LIL is similar to other studies in the literature; conversely, the lower half is substantially different. In particular, we show that, due to the failure of the classical version of the second Borel-Cantelli lemma, the upper and the lower bounds are separated, with the lower bound being further and further away as the memory of the sequence increases.