no. 11-12
Probabilités
On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants
Thành, Lê Vǎn1
1 Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam
Comptes Rendus. Mathématique, Tome 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
Thành, Lê Vǎn 1

1 Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam 
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Thành, Lê Vǎn. On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1231-1238. doi : 10.5802/crmath.139. http://www.numdam.org/articles/10.5802/crmath.139/

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