Previous |  Up |  Next

Article

Keywords:
strong law of large numbers; convex combination space; pairwise $m$-dependent; blockwise $m$-dependent; compactly uniformly integrable
Summary:
The aim of the paper is to establish strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables in a convex combination space with or without compactly uniformly integrable condition. Some of our results are even new in the case of real random variables.
References:
[1] Bo, Z.: Marcinkiewicz-Zygmund law for sequences of blockwise $m$-dependent random variables. Statist. Probab. Lett. 38 (1998), 83-88. DOI 10.1016/S0167-7152(97)00157-0 | MR 1629524 | Zbl 0908.60009
[2] Choi, B. D., Sung, S. H.: On convergence of $(S_n -ES_n)/n^{1/r}$, $1. Bull. Korean Math. Soc. 22 (1985), 79-82. MR 0826361
[3] Etemadi, N.: An elementary proof of the strong law of large numbers. Z. Wahrscheinlichkeitstheor. Verw. Geb. 55 (1981), 119-122. DOI 10.1007/BF01013465 | MR 0606010 | Zbl 0438.60027
[4] Gaposhkin, V. F.: On the strong law of large numbers for blockwise independent and blockwise orthogonal random variables. Theory Probab. Appl. 39 677-684 (1994), translation from Teor. Veroyatn. Primen. Russian 39 804-812 (1994). DOI 10.1137/1139053 | MR 1347654 | Zbl 0847.60022
[5] Móricz, F.: Strong limit theorems for blockwise $m$-dependent and blockwise quasi-orthogonal sequences of random variables. Proc. Am. Math. Soc. 101 (1987), 709-715. DOI 10.2307/2046676 | MR 0911038
[6] Quang, N. V., Thuan, N. T.: On the strong laws of large numbers for double arrays of random variables in convex combination spaces. Acta Math. Hung. 134 (2012), 543-564. DOI 10.1007/s10474-011-0168-1 | MR 2886225 | Zbl 1265.60057
[7] Terán, P., Molchanov, I.: The law of large numbers in a metric space with a convex combination operation. J. Theor. Probab. 19 (2006), 875-898. DOI 10.1007/s10959-006-0043-0 | MR 2279607 | Zbl 1113.60014
[8] Thanh, L. V.: Strong laws of large numbers for sequences of blockwise and pairwise $m$-dependent random variables. Bull. Inst. Math., Acad. Sin. 33 (2005), 397-405. MR 2184437 | Zbl 1084.60506
[9] Thuan, N. T., Quang, N. V., Nguyen, P. T.: Complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces. Fuzzy Sets Syst. 250 (2014), 52-68. MR 3223442 | Zbl 1334.60041
Partner of
EuDML logo