Equivalent conditions of the complete convergence for weighted sums of NSD random variables
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Cited by 2 publications
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In this work, suppose that {X n ; n ≥ 1}is a sequence of asymptotically negatively associated random variables and {a ni ; 1 ≤ i ≤ n, n ≥ 1} is an array of real numbers such that ∑ i = 1 n | a n i | q = O ( n ) for some q > max { α p − 1 α − 1 / 2 , 2 } with αp > 1 and α > 1 2 . Let l (x) > 0 be a slowly varying function at infinity. We establish some equivalent conditions of the complete convergence for weighted sums of this form ∑ n = 1 ∞ n α p − 2 l ( n ) P ( max 1 ≤ j ≤ n | ∑ i = 1 j a n i X i | > ε n α ) < ∞ for all ε > 0 . As applications, some strong laws of large numbers for weighted sums of asymptotically negatively associated random variables are also obtained.
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