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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
##### Keywords:
subsequence; complete convergence