New asymptotic results for generalized Oppenheim expansions

TL;DR

This paper investigates convergence properties of weighted partial sums of certain infinite-mean random variables related to generalized Oppenheim expansions, providing new asymptotic results without assuming dependence.

Contribution

It introduces novel asymptotic results for convergence in probability and almost sure convergence for these variables, expanding understanding without dependence assumptions.

Findings

Convergence in probability established for weighted sums.

Almost sure convergence demonstrated under new conditions.

Results applicable to variables with infinite mean.

Abstract

In this work, 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.