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Quick and Complete Convergence in the Law of Large Numbers with Applications to Statistics
Mathematics, 2023 In the first part of this article, we discuss and generalize the complete convergence introduced by Hsu and Robbins in 1947 to the r-complete convergence introduced by Tartakovsky in 1998.
Alexander G. Tartakovsky
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Moment Inequalities and Complete Moment Convergence
Journal of Inequalities and Applications, 2009 Let \(\{Y_i\), \(1\leq i\leq n\}\) and \(\{Z_i\), \(1\leq i\leq n\}\) be sequences of random variables. For any \(\varepsilon> 0\) and \(a> 0\), bounds for \[ E\Biggl(\Biggl| \sum^n_{i=1} (Y_i+ Z_i)\Biggr|-\varepsilon a\Biggr)^+ \] and \[ E\Biggl(\max_{1\leq k\leq n}\Biggl|\sum^k_{i= 1} (Y_i+ Z_i)\Biggr|-\varepsilon a\Biggr)^+ \] are obtained.
Sung SooHak
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On complete convergence in a Banach space [PDF]
International Journal of Mathematics and Mathematical Sciences, 1994 Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers.
Dominik Szynal, Anna Kuczmaszewska
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Filomat, 2017 In this paper, we provide some probability and moment inequalities (especially the Marcinkiewicz-Zygmund type inequality) for extended negatively dependent (END, in short) random variables.
Aiting Shen, Yu. Zhang, Wenjuan Wang
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Complete convergence for arrays of minimal order statistics [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 For arrays of independent Pareto random variables, this paper establishes complete convergence for weighted partial sums for the smaller order statistics within each row. This result improves on past strong laws.
André Adler, André Adler
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Complete Convergence for Negatively Dependent Sequences of Random Variables [PDF]
Journal of Inequalities and Applications, 2010 We study the complete convergence for negatively dependent sequences of random variables. As a result, we extend some complete convergence theorems for independent random variables to the case of negatively dependent random variables without necessarily ...
Wu Qunying, Qunying Wu
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ON COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE FOR A CLASS OF RANDOM VARIABLES
Journal of the Korean Mathematical Society, 2017 Xuejun Wang, Yi Wu
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Complete Convergence for Moving Average Process of Martingale Differences [PDF]
Discrete Dynamics in Nature and Society, 2012 Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete ...
Shuhe Hu, Xuejun Wang, Wenzhi Yang
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Complete Convergence for END Random Variables under Sublinear Expectations [PDF]
Discrete Dynamics in Nature and Society, 2021 In this paper, the complete convergence theorems of partial sums and weighted sums for extended negatively dependent random variables in sublinear expectation spaces have been studied and established.
Qunying Wu
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On the Complete Convergence of Martingale
Mathematica Pannonica, 2023 In the present paper, we establish the convergence rates of the single logarithm and the iterated logarithm for martingale differences which give some further results for the open question in Stoica [6].
Chang, Mengmeng, Miao, Yu
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