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

Trapani, Lorenzo

Authors



Abstract

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.

Journal Article Type Article
Publication Date Dec 15, 2014
Journal Journal of Mathematical Analysis and Applications
Print ISSN 0022-247X
Electronic ISSN 0022-247X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 420
Issue 2
APA6 Citation 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
DOI https://doi.org/10.1016/j.jmaa.2014.06.042
Keywords Chover Law of the Iterated Logarithm; Strongly mixing sequence of random variables; Slowly varying function
Publisher URL http://www.sciencedirect.com/science/article/pii/S0022247X14005897
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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