Abstract
Let{Xni,i≥1,n≥1}be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables is obtained.
Highlights
IntroductionThe concept of complete convergence was introduced by Hsu and Robbins 1 as follows
The concept of complete convergence was introduced by Hsu and Robbins 1 as follows.A sequence of random variables {Un, n ≥ 1} is said to converge completely to a constant C if ∞ n |Un − C| > ε< ∞ for all ε > 0
Our goal in this paper is to study the complete convergence for arrays of rowwise AANA random variables under some moment conditions
Summary
The concept of complete convergence was introduced by Hsu and Robbins 1 as follows. A sequence of random variables {Un, n ≥ 1} is said to converge completely to a constant C if. Hsu and Robbins 1 proved that the sequence of arithmetic means of independent and identically distributed i.i.d. random variables converges completely to the expected value if the variance of the summands is finite. Since many authors studied the complete convergence for partial sums and weighted sums of random variables. The main purpose of the present investigation is to provide the complete convergence results for weighted sums of asymptotically almost negatively associated random variables and arrays of rowwise asymptotically almost negatively associated random variables. Let us recall the definitions of negatively associated and asymptotically almost negatively associated random variables
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