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New asymptotic results for generalized Oppenheim expansions

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Abstract

We study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables under study have infinite mean and the results are obtained without any dependence assumptions.

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Acknowledgement

R. Giuliano wishes to thank UCLan Cyprus and the University of Cyprus for their hospitality; part of the present paper was completed during her visit in Cyprus.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127, Pisa, Italy

    R. Giuliano

  2. School of Sciences, University of Central Lancashire, Cyprus campus, 12-14 University Avenue, Larnaka, 7080, Cyprus

    M. Hadjikyriakou

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  1. R. Giuliano
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  2. M. Hadjikyriakou
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Correspondence to M. Hadjikyriakou.

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Part of this work was conducted while the second author was a visiting scholar at the University of Cyprus.

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Giuliano, R., Hadjikyriakou, M. New asymptotic results for generalized Oppenheim expansions. Acta Math. Hungar. 169, 359–381 (2023). https://doi.org/10.1007/s10474-023-01321-x

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  • DOI: https://doi.org/10.1007/s10474-023-01321-x

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