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