On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants

Lê Vǎn Thành

doi:10.5802/crmath.139

Probabilités

On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants

Lê Vǎn Thành ¹

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.

Résumé

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.

Reçu le : 2020-06-05
Révisé le : 2020-11-05
Accepté le : 2020-11-07
Publié le : 2021-01-25

DOI : 10.5802/crmath.139

Classification : 60F15

Affiliations des auteurs :

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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     author = {L\^e Vǎn Th\`anh},
     title = {On the {Baum{\textendash}Katz} theorem for sequences of pairwise independent random variables with regularly varying normalizing constants},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1231--1238},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.139},
     language = {en},
}

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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/

Bibliographie
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