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Wu, Yong-Feng; Ding, Hui

On the complete convergence for arrays of rowwise \({\psi}\)-mixing random variables. (English) Zbl 1290.60042

J. Inequal. Appl. 2013, Paper No. 393, 9 p. (2013).
Summary: Some sufficient conditions for complete convergence for maximal weighted sums \(\max_{1 \leq j \leq n} |\sum_{k=1}^j a_{nk}X_{nk}|\) and weighted sums \(\sum_{k=1}^n a_{nk}X_{nk}\) are presented, where \(\{X_{nk}: 1 \leq k \leq n, \, n \geq 1\}\) is an array of rowwise \(\psi\)-mixing random variables, and \(\{a_{nk}: 1 \leq k \leq n, \, n \geq 1\}\) is an array of constants. The obtained results extend and improve the corresponding result in the previous literature.

MSC:

60F15 Strong limit theorems

Keywords:

\(\psi\)-mixing random variable; weighted sums; complete convergence
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References:

[1] doi:10.1073/pnas.33.2.25 · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25
[2] doi:10.1007/BF00535293 · Zbl 0117.35603 · doi:10.1007/BF00535293
[3] doi:10.1214/aoms/1177693079 · Zbl 0226.60008 · doi:10.1214/aoms/1177693079
[4] doi:10.1080/07362998708809124 · Zbl 0633.60049 · doi:10.1080/07362998708809124
[5] doi:10.1137/1135013 · Zbl 0724.60028 · doi:10.1137/1135013
[6] doi:10.1214/aop/1176990445 · Zbl 0735.60034 · doi:10.1214/aop/1176990445
[7] doi:10.1016/0304-4149(93)90051-5 · Zbl 0793.60038 · doi:10.1016/0304-4149(93)90051-5
[8] doi:10.1016/j.spl.2008.07.026 · Zbl 1154.60026 · doi:10.1016/j.spl.2008.07.026
[9] doi:10.1016/j.spl.2009.10.018 · Zbl 1186.60031 · doi:10.1016/j.spl.2009.10.018
[10] doi:10.1016/j.aml.2010.04.010 · Zbl 1197.60031 · doi:10.1016/j.aml.2010.04.010
[11] doi:10.1155/2010/372390 · Zbl 1208.60031 · doi:10.1155/2010/372390
[12] doi:10.1007/BF01950716 · Zbl 0685.60032 · doi:10.1007/BF01950716
[13] doi:10.1081/SAP-120004118 · Zbl 1003.60032 · doi:10.1081/SAP-120004118
[14] doi:10.4134/JKMS.2009.46.4.827 · Zbl 1175.60024 · doi:10.4134/JKMS.2009.46.4.827
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