Abstract
Let \(\{a_{n}, n \geq 1\}\) be a sequence of positive numbers and \(\{X, X_{n}, n \geq 1\}\) be a sequence of identically distributed random variables. The strong law of large numbers and complete convergence for the partial sums of the random sequence \(\{X, X_{n}, n \geq 1\}\) are established under the mild moment condition \(\sum\nolimits^{\infty}_{n=1} \mathbb{P}(|X| > a_{n})<\infty\) and under general dependence conditions. These results generalize and extend some known works.
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This work is supported by National Natural Science Foundation of China (NSFC-11971154).
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Miao, Y., Shi, J. & Yu, Z. On the complete convergence and strong law for dependent random variables with general moment conditions. Acta Math. Hungar. 168, 425–442 (2022). https://doi.org/10.1007/s10474-022-01284-5
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DOI: https://doi.org/10.1007/s10474-022-01284-5
Key words and phrases
- strong law of large numbers
- complete convergence
- positively associated random variable
- asymptotically almost negatively associated sequence