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The complete convergence of subsequences for sums of independent random variables. (Chinese. English summary) Zbl 0781.60026
Summary: Let \(\{X_ n, n\geq 1\}\) be i.i.d. random variables and \(S_ n = \sum^ n_{i=1}X_ i\), let \(\{a_ n, n\geq 1\}\) be a sequence of real numbers tending to infinity, and \(\{n_ k\}\) the strictly increasing subsequence of positive integer numbers. We give necessary and sufficient conditions of complete convergence for \(S_{n_ k}/a_{n_ k}\) and obtain the complete convergence for sums of random variables.

MSC:
60F15 Strong limit theorems
60G50 Sums of independent random variables; random walks
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