Convergence rates for weighted sums of random variables with random indices
D. Szynal, A. Zapała (1977)
Colloquium Mathematicae
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D. Szynal, A. Zapała (1977)
Colloquium Mathematicae
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Zdzisław Rychlik (1976)
Colloquium Mathematicae
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Haiwu Huang, Xuewen Lu (2020)
Applications of Mathematics
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In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the assumption of identical distribution. As an application, a Marcinkiewicz-Zygmund-type...
Z. Rychlik, D. Szynal (1973)
Colloquium Mathematicae
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M. Ordóñez Cabrera (1989)
Extracta Mathematicae
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Haiwu Huang, Hanjun Zhang, Qingxia Zhang, Jiangyan Peng (2015)
Kybernetika
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In this paper, the authors further studied the complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated (AANA) random variables with non-identical distribution under some mild moment conditions. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of AANA random variables is obtained. The results not only generalize the corresponding ones of Wang et al. [19], but also partially improve the corresponding...
Haiwu Huang, Linyan Li, Xuewen Lu (2020)
Kybernetika
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In this research, strong convergence properties of the tail probability for weighted sums of negatively orthant dependent random variables are discussed. Some sharp theorems for weighted sums of arrays of rowwise negatively orthant dependent random variables are established. These results not only extend the corresponding ones of Cai [4], Wang et al. [19] and Shen [13], but also improve them, respectively.
Xinghui Wang, Xiaoqin Li, Shuhe Hu (2014)
Applications of Mathematics
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In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise -mixing random variables, and the Baum-Katz-type result for arrays of rowwise -mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of -mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).
Slobodanka Janković (1990)
Publications de l'Institut Mathématique
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Jan Rosiński (1975)
Colloquium Mathematicae
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