Remarks on Yu Miao and Shoufang Xu's paper "almost sure convergence of weighted sums"

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Abstract

It is pointed out that a general theorem presented in Yu Miao and Shoufang Xu's paper has a serious gap. In this small note, a counterexample for this theorem is provided exhibiting a triangular array of real numbers and a sequence of independent identically distributed random variables for which its conclusion fails. An reformulation of Yu Miao and Shoufang Xu's general theorem is performed making this statement true.

Original languageEnglish
Pages (from-to)503-506
Number of pages4
JournalMiskolc Mathematical Notes
Volume16
Issue number1
Publication statusPublished - 2015

Keywords

  • Almost sure convergence
  • Triangular arrays
  • Weighted sums

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