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On the Brunk-Chung type strong law of large numbers forsequences of blockwise m-dependent random variables
Published online by Cambridge University Press: 03 May 2006
Abstract
For a sequence of blockwise m-dependent random variables {Xn,n ≥ 1}, conditions are provided under which $\lim_{n\to\infty}(\sum_{i=1}^nX_i)/b_n=0$ almost surely where {bn,n ≥ 1} is a sequence of positive constants. The results are new even when bn ≡ nr,r > 0. As special case, the Brunk-Chung strong law of large numbers is obtained for sequences of independent random variables. The current work also extends results of Móricz [Proc. Amer. Math. Soc.101 (1987) 709–715], and Gaposhkin [Teor. Veroyatnost. i Primenen. 39 (1994) 804–812]. The sharpness of the results is illustrated by examples.
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- © EDP Sciences, SMAI, 2006
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