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On the Baum-Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants
Authors: Lê Văn Thành
443    1
Comptes Rendus Mathématique
: 11-12     : 1231--1238
: https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_11-12_1231_0/
: 1523_2020 Comptes Rendus Math.pdf
Publishing year: 12/2020
This paper proves the Baum–Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditions. The proof exploits some properties of slowly varying functions and the de Bruijn conjugates, and uses the techniques developed by Rio (1995) to avoid using the maximal type inequalities.
Strong law of large numbers, Rate of convergence, Pairwise independence
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