Abstract
In the paper, we study the strong law of large numbers for general weighted sums of asymptotically almost negatively associated random variables (AANA, in short) with non-identical distribution. As an application, the Marcinkiewicz strong law of large numbers for AANA random variables is obtained. In addition, we present some sufficient conditions to prove the strong law of large numbers for weighted sums of AANA random variable. Our results generalize the corresponding ones (sufficient conditions) for independent random variables. MSC: 60F15
Highlights
Throughout the paper, let {X, Xn, n ≥ } be a sequence of random variables defined on a fixed probability space (, F, P)
Sung [ ] gave some sufficient conditions to prove the strong law of large numbers for weighted sums of random variables
We present some sufficient conditions to prove the strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables
Summary
Throughout the paper, let {X, Xn, n ≥ } be a sequence of random variables defined on a fixed probability space ( , F , P). Let {Xn, n ≥ } be a sequence of independent and identically distributed random variables. Sung [ ] gave some sufficient conditions to prove the strong law of large numbers for weighted sums of random variables. We present some sufficient conditions to prove the strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables.
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