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Remarks on Yu Miao and Shoufang Xu's paper "almost sure convergence of weighted sums"
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Resumo(s)
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.
Descrição
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).
Palavras-chave
Almost sure convergence Triangular arrays Weighted sums Algebra and Number Theory Analysis Control and Optimization Discrete Mathematics and Combinatorics Numerical Analysis