Law of the logarithm and law of the iterated logarithm for a class of random variables with non-identical distributions

Haichao Yu and Yong Zhang

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 22, 8169-8183

Abstract: Let {Yn,n≥1} be sequence of random variables with EYn = 0. Assume that the Kolmogrov type exponential inequality is satisfied for {Yxj=−xI{Yj x},j≥1} with any x > 0. In this paper, the law of the logarithm and law of the iterated logarithm for a class of random variables satisfying the Kolmogrov type exponential inequality with non-identical distributions are obtained. The main results not only extend the known results from NA case to a class of random variables satisfying Kolmogrov type exponential inequality, but also weaken the moment assumptions.

Date: 2023
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DOI: 10.1080/03610926.2022.2059680

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