The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences

@article{Anh2019TheMS,
  title={The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences},
  author={Vu T. N. Anh and Nguyen Thi Hien and Le Van Thanh and Vo Thi Hong Van},
  journal={Journal of Theoretical Probability},
  year={2019},
  volume={34},
  pages={331-348}
}
This paper establishes complete convergence for weighted sums and the Marcinkiewicz–Zygmund-type strong law of large numbers for sequences of negatively associated and identically distributed random variables $$\{X,X_n,n\ge 1\}$$ { X , X n , n ≥ 1 } with general normalizing constants under a moment condition that $$ER(X)<\infty $$ E R ( X ) < ∞ , where $$R(\cdot )$$ R ( · ) is a regularly varying function. The result is new even when the random variables are independent and identically… 
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