On exact laws of large numbers for Oppenheim expansions with infinite mean

Rita Giuliano; Milto Hadjikyriakou

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arXiv · 2004.02992

On exact laws of large numbers for Oppenheim expansions with infinite mean

Rita Giuliano·Milto Hadjikyriakou

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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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Rita Giuliano, Milto Hadjikyriakou. 2020-04-06. On exact laws of large numbers for Oppenheim expansions with infinite mean. https://arxiv.org/abs/2004.02992

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