Chover-type laws of the k -iterated logarithm for weighted sums of strongly mixing sequences
نویسنده
چکیده
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.
منابع مشابه
CHOVER-TYPE LAWS OF THE ITERATED LOGARITHM FOR WEIGHTED SUMS OF rhoast-MIXING SEQUENCES
We call this a Chover-type LIL (laws of the iterated logarithm). This type LIL has been established by Vasudeva and Divanji [13], Zinchenko [14] for delayed sums, by Chen and Huang [3] for geometric weighted sums, and by Chen [2] for weighted sums. Qi and Cheng [11] extended the Chover-type law of the iterated logarithm for the partial sums to the case where the underlying distribution is in th...
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