Complete convergence for arrays

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1992 English Publisher:Springer Science and Business Media LLCJournal:Periodica Mathematica Hungarica, volume 25, pages 51-75 (issn: 0031-5303, eissn: 1588-2829,

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Authors: Gut, A.;

doi: 10.1007/bf02454383

Complete convergence for arrays

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Abstract

Let \(\{(X_{nk}\), \(1\leq k\leq n)\), \(n\geq 1\}\) be an array of rowwise independent random variables. We extend and generalize some recent results due to \textit{T.-C. Hu}, \textit{F. Móricz} and \textit{R. L. Taylor} [Acta Math. Hung. 54, No. 1/2, 153-162 (1989; Zbl 0685.60032)] concerning complete convergence, in the sense of \textit{P. L. Hsu} and \textit{H. Robbins} [Proc. Natl. Acad. Sci. USA 33, 25-31 (1947; Zbl 0030.20101)], of the sequence of rowwise arithmetic means.

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Uppsala University
Sweden

Keywords

array of rowwise independent random variables, Strong limit theorems, Sums of independent random variables; random walks, strong law, complete convergence, central limit theorem, weighted sums

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