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

Rita Giuliano () and Milto Hadjikyriakou ()
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Rita Giuliano: Università di Pisa
Milto Hadjikyriakou: University of Central Lancashire

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1579-1606

Abstract: 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.

Keywords: Oppenheim expansions; Exact strong laws; Exact weak laws; Infinite means; 60F15; 60F05; 11K55 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01010-3

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