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.
Trapani, L. (2014). Chover-type laws of the k-iterated logarithm for weighted sums of strongly mixing sequences. Journal of Mathematical Analysis and Applications, 420(2), doi:10.1016/j.jmaa.2014.06.042