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MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES
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 Title & Authors
MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES
Xuejun, Wang; Shuhe, Hu; Xiaoqin, Li; Wenzhi, Yang;
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 Abstract
Let {, } be a sequence of asymptotically almost negatively associated random variables and . In the paper, we get the precise results of Hjek-Rnyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.
 Keywords
Hjek-Rnyi inequality;asymptotically almost negatively associated sequence;strong law of large numbers;large deviation;
 Language
English
 Cited by
1.
On a General Approach to the Strong Laws of Large Numbers*, Journal of Mathematical Sciences, 2014, 200, 4, 411  crossref(new windwow)
2.
Complete Convergence of the Maximum Partial Sums for Arrays of Rowwise of AANA Random Variables, Discrete Dynamics in Nature and Society, 2013, 2013, 1  crossref(new windwow)
3.
Maximal inequalities and strong law of large numbers for sequences of m-asymptotically almost negatively associated random variables, Communications in Statistics - Theory and Methods, 2017, 46, 6, 2696  crossref(new windwow)
4.
Strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2015, 109, 1, 135  crossref(new windwow)
5.
Strong Convergence Properties and Strong Stability for Weighted Sums of AANA Random Variables, Abstract and Applied Analysis, 2013, 2013, 1  crossref(new windwow)
6.
Lr convergence for arrays of rowwise asymptotically almost negatively associated random variables, Communications in Statistics - Theory and Methods, 2017, 0  crossref(new windwow)
 References
1.
T. K. Chandra and S. Ghosal, Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hungar. 71 (1996), no. 4, 327-336. crossref(new window)

2.
T. K. Chandra and S. Ghosal, The strong law of large numbers for weighted averages under dependence assumptions, J. Theoret. Probab. 9 (1996), no. 3, 797-809. crossref(new window)

3.
I. Fazekas and O. Klesov, A general approach to the strong laws of large numbers, Teor. Veroyatnost. i Primenen. 45 (2000), no. 3, 568-583; translation in Theory Probab. Appl. 45 (2002), no. 3, 436-449. crossref(new window)

4.
M. H. Ko, T. S. Kim, and Z. Y. Lin, The Hajeck-Renyi inequality for the AANA random variables and its applications, Taiwanese J. Math. 9 (2005), no. 1, 111-122.

5.
Y. B. Wang, J. G. Yan, and F. Y. Cheng, The strong law of large numbers and the law of the iterated logarithm for product sums of NA and AANA random variables, Southeast Asian Bull. Math. 27 (2003), no. 2, 369-384.

6.
D. M. Yuan and J. An, Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications, Sci. China Ser. A 52 (2009), no. 9, 1887-1904. crossref(new window)