Comptes Rendus
no. 11-12
Probabilités
On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants
Lê Vǎn Thành1
1 Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1231-1238.

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.

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Révisé le :
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DOI : 10.5802/crmath.139
Classification : 60F15
Lê Vǎn Thành 1

1 Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Comptes Rendus. Math\'ematique},
     pages = {1231--1238},
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Lê Vǎn Thành. On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1231-1238. doi : 10.5802/crmath.139. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.139/

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