A Law of the Iterated Logarithm for the Signum Function

Santosh Ghimire

doi:10.52783/cana.v32.1747

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Published: Sep 26, 2024

DOI: https://doi.org/10.52783/cana.v32.1747

Keywords:

Signum functions, q-lacunary series, law of the iterated logarithm, Borel-Cantelli lemma.

Santosh Ghimire

Abstract

In 2023, S. Ghimire established a one-sided version of a law of the iterated logarithm, denoted as LIL, for summations of signum functions analogous to the LIL proposed by Salem and Zygmund for trigonometric series. In this article, we complete the LIL for these signum functions by establishing the complimentary version of the LIL.

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Vol. 32 No. 2 (2025)

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