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On Exact Laws of Large Numbers for Oppenheim Expansions with Infinite Mean

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Giuliano, Rita and Hadjikyriakou, Milto ORCID: 0000-0001-5672-7792 (2021) On Exact Laws of Large Numbers for Oppenheim Expansions with Infinite Mean. Journal of Theoretical Probability, 34 . pp. 1579-1606. ISSN 0894-9840

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Official URL: https://doi.org/10.1007/s10959-020-01010-3

Abstract

In this work we investigate the asymptotic behaviour of weighted partial sums of a particular class of random variables related to Oppenheim series expansions. More precisely, we verify convergence in probability as well as almost sure convergence to a strictly positive and ﬁnite constant without assuming any dependence structure or the existence of means. Results of this kind are known as exact weak and exact strong laws.

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