MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES

Wang Xuejun, Hu Shuhe, Li Xiaoqin, Yang Wenzhi
2011 Communications of the Korean Mathematical Society  
Let {Xn, n ≥ 1} be a sequence of asymptotically almost negatively associated random variables and Sn = ∑ n i=1 X i . In the paper, we get the precise results of Hájek-Rényi 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 Sn for sequence of asymptotically almost negatively associated random variables is studied. At last, the
more » ... ied. At last, the Marcinkiewicz type strong law of large numbers is given. ( whenever f and g are coordinatewise nondecreasing such that this covariance exists. An infinite sequence {X n , n ≥ 1} is NA if every finite subcollection is NA. Definition 1.2. A sequence {X n , n ≥ 1} of random variables is called asymptotically almost negatively associated (AANA, in short) if there exists a nonnegative sequence q(n) → 0 as n → ∞ such that Cov(f (X n ), g(X n+1 , X n+2 , . . . , X n+k )) ≤ q(n) [V ar(f (X n ))V ar(g(X n+1 , X n+2 , . . . , X n+k ))]
doi:10.4134/ckms.2011.26.1.151 fatcat:3mfehpakozhj5lpzcxzfffwshe