Maximal inequalities and strong law of large numbers for AANA sequences
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Let {X_n, n≥1} be a sequence of asymptotically almost negatively associated random variables and S_n=(수식)X_i. In the paper, we get the precise results of H(특수문자)jek-R(특수문자)nyi 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 S_n for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.
Abstract
Let {X_n, n≥1} be a sequence of asymptotically almost negatively associated random variables and S_n=(수식)X_i. In the paper, we get the precise results of H(특수문자)jek-R(특수문자)nyi 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 S_n for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.
참고문헌 (6)
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- M. H. Ko, "The Hajeck-Renyi inequality for the AANA random variables and its applications", Taiwanese J. Math, 9(1), pp.111~122 (2005)
- Y. B. Wang, "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(2), pp.369~384 (2003)
- D. M. Yuan, "Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications", Sci. China Ser. A, 52(9), pp.1887~1904 (2009)