Limit theorems for dependent random variables with infinite means

Ismahen Bernou and Fakhreddine Boukhari

Statistics & Probability Letters, 2022, vol. 189, issue C

Abstract: We investigate necessary and sufficient conditions for the convergence in probability of weighted averages of random variables with infinite means. The obtained results are valid for a wide range of dependence structures, they extend and improve the corresponding theorems of Adler (2012) and Nakata (2016), established in the independent case.

Keywords: Weak laws; Weighted exact laws; Pareto-type distributions Rosenthal–type maximal inequalities; St. Petersburg game; Feller game (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109563

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