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

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Almost Sure Convergence
Weighted Sums
Random variables
Theorem
Triangular Array
Reformulation
Identically distributed
Counterexample
Random variable

Keywords

  • Almost sure convergence
  • Triangular arrays
  • Weighted sums

Cite this

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title = "Remarks on Yu Miao and Shoufang Xu's paper {"}almost sure convergence of weighted sums{"}",
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.",
keywords = "Almost sure convergence, Triangular arrays, Weighted sums",
author = "{da Silva}, {Jo{\~a}o Lita}",
note = "This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UI0297/2014 (Centro de Matematica e Aplicacoes).",
year = "2015",
language = "English",
volume = "16",
pages = "503--506",
journal = "Miskolc Mathematical Notes",
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}

Remarks on Yu Miao and Shoufang Xu's paper "almost sure convergence of weighted sums". / da Silva, João Lita.

In: Miskolc Mathematical Notes, Vol. 16, No. 1, 2015, p. 503-506.

Research output: Contribution to journalArticle

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AU - da Silva, João Lita

N1 - This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PEst-OE/MAT/UI0297/2014 (Centro de Matematica e Aplicacoes).

PY - 2015

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N2 - 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.

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KW - Triangular arrays

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