| Issue |
ESAIM: PS
Volume 10, September 2006
|
|
|---|---|---|
| Page(s) | 258 - 268 | |
| DOI | https://doi.org/10.1051/ps:2006010 | |
| Published online | 03 May 2006 | |
On the Brunk-Chung type strong law of large numbers for sequences of blockwise m-dependent random variables
Department of Mathematics, Vinh University, Vinh, Nghe An 42118, Vietnam. lvthanhvinh@yahoo.com
Received:
5
September
2005
For a sequence of blockwise m-dependent random variables {Xn,n ≥ 1}, conditions are provided under which 
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.
Mathematics Subject Classification: 60F15
Key words: Strong law of large numbers / almost sure convergence / blockwise m-dependent random variables.
© EDP Sciences, SMAI, 2006
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