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

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), pp. 908-916. doi: 10.1016/j.jmaa.2014.06.042

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.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, Volume 420, Issue 2, 15 December 2014, Pages 908–916, http://dx.doi.org/10.1016/j.jmaa.2014.06.042
Publisher Keywords: Chover Law of the Iterated Logarithm; Strongly mixing sequence of random variables; Slowly varying function
Subjects: H Social Sciences > HG Finance
Departments: Cass Business School > Finance
Related URLs:
URI: http://openaccess.city.ac.uk/id/eprint/6105
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