Abstract
Let { X n i , 1 ≤ i ≤ n , n ≥ 1 } Open image in new window be an array of random variables with E X n i = 0 Open image in new window and E | X n i | q 0 Open image in new window, where x + = max { x , 0 } Open image in new window. From these results, we can easily obtain some known results on complete q th moment convergence.
Highlights
1 Introduction The concept of complete convergence was introduced by Hsu and Robbins [ ]
The complete qth moment convergence for dependent random variables was established by many authors
The purpose of this paper is to provide sets of sufficient conditions for complete qth moment convergence of the form
Summary
The concept of complete convergence was introduced by Hsu and Robbins [ ]. A sequence {Xn, n ≥ } of random variables is said to converge completely to the constant θ if If {Xn, n ≥ } is a sequence of i.i.d. random variables with EX = and < p < , t ≥ , q > , and pt ≥ , the moment condition
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