On the Brunk-Chung type strong law of large numbers for sequences of blockwise m-dependent random variables
ESAIM: Probability and Statistics, Tome 10 (2006), pp. 258-268

For a sequence of blockwise m-dependent random variables {X n ,n≥1}, conditions are provided under which lim n→∞ (∑ i=1 n X i )/b n =0 almost surely where {b n ,n≥1} is a sequence of positive constants. The results are new even when b n ≡n r ,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.

DOI : 10.1051/ps:2006010
Classification : 60F15
Keywords: strong law of large numbers, almost sure convergence, blockwise $m$-dependent random variables 
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     title = {On the {Brunk-Chung} type strong law of large numbers for sequences of blockwise $m$-dependent random variables},
     journal = {ESAIM: Probability and Statistics},
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     url = {https://www.numdam.org/articles/10.1051/ps:2006010/}
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Thanh, Le Van. On the Brunk-Chung type strong law of large numbers for sequences of blockwise $m$-dependent random variables. ESAIM: Probability and Statistics, Tome 10 (2006), pp. 258-268. doi: 10.1051/ps:2006010

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