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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Lê Vǎn Thành 1
@article{CRMATH_2020__358_11-12_1231_0, 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}, }
TY - JOUR AU - Lê Vǎn Thành TI - On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants JO - Comptes Rendus. Mathématique PY - 2020 SP - 1231 EP - 1238 VL - 358 IS - 11-12 PB - Académie des sciences, Paris DO - 10.5802/crmath.139 LA - en ID - CRMATH_2020__358_11-12_1231_0 ER -
%0 Journal Article %A Lê Vǎn Thành %T On the Baum–Katz theorem for sequences of pairwise independent random variables with regularly varying normalizing constants %J Comptes Rendus. Mathématique %D 2020 %P 1231-1238 %V 358 %N 11-12 %I Académie des sciences, Paris %R 10.5802/crmath.139 %G en %F CRMATH_2020__358_11-12_1231_0
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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