A note on complete convergence for arrays. (English) Zbl 0910.60017
Stat. Probab. Lett. 38, No. 1, 27-31 (1998); addendum ibid. 47, No. 2, 209-211 (2000).
Summary: We extend and generalize some recent results on complete convergence for independent non-identically distributed random variables [cf. R. Duncan and D. Szynal, Bull. Pol. Acad. Sci., Math. 32, 729-735 (1984; Zbl 0564.60026); A. Gut, Period. Math. Hung. 25, No. 1, 51-75 (1992; Zbl 0760.60029); T. C. Hu, F. Moricz and R. L. Taylor, Acta Math. Hung. 54, No. 1/2, 153-162 (1989; Zbl 0685.60032)]. In the main result no assumptions are made concerning the existence of expected values or absolute moments of the random variables. Some well-known results from the literature can be easily obtained from our theorem.
Keywords:
rowwise independence; sums of independent random variables; complete convergence; strong law of large numbersReferences:
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| [5] | Hu, T. C.; Moricz, F.; Taylor, R. L., Strong law of large numbers for arrays of rowwise independent random variables, Acta Math. Acad. Sci. Hungar., 54, 153-162 (1989) · Zbl 0685.60032 |
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