Abstract
In this paper, we present some general results concerning complete convergence for arrays of dependent random variables, dominated in a sense by independent random variables. As an application, we obtain the Baum–Katz-type theorem for arrays of some class of dependent random variables.
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References
Chen P, Hu TC, Liu X, Volodin A (2008) On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl 52(2):323–328
Çelebioǧlu S (1997) A way of generating comprehensive copulas. Gazi Univ J Sci 10(1):57–61
Cuadras CM (2009) Constructing copula functions with weighted geometric means. J Stat Plan Inference 139:3766–3772
Erdös P (1949) On a theorem of Hsu and Robbins. Ann Math Stat 20:286–291
Gut A (1992) Complete convergence for arrays. Period Math Hungar 25:51–75
Hsu PL, Robbins H (1947) Complete convergence and the law of large numbers. Natl Acad Sci USA 33:25–31
Hu TC, Szynal D, Volodin A (1998) A note on complete convergence for arrays. Stat Probab Lett 38:27–31
Hu TC, Rosalsky A, Wang KL (2015) Complete convergence theorems for extended negatively dependent random variables. Sankhy\(\bar{a}\) A Indian J Stat 77-A (1):1–29
Kruglov VM, Volodin A, Hu TC (2006) On complete convergence for arrays. Stat Probab Lett 76:1631–1640
Kuczmaszewska A, Lagodowski ZA (2011) Convergence rates in the SLLN for some classes of dependent random fields. J Math Anal Appl 380(2):571–584
Naderi H, Matuła P, Amini M, Bozorgnia A (2016) On stochastic dominance and the strong law of large numbers for dependent random variables. RACSAM 110(2):771–782
Petrov VV (1995) Limit theorems of probability theory. Oxford studies in probability. Clarendon Press, Oxford
Qiu DH, Chang KC, Giuliano AR, Volodin A (2011) On the strong rates of convergence for arrays of rowwise negatively dependent random variables. Stoch Anal Appl 29:375–385
Shen A, Yao M, Wang W, Volodin A (2016) Exponential probability inequalities for WNOD random variables and their applications. RACSAM 110(1):251–268
Szewczak ZS (2013) On the maximal Lévy-Ottaviani inequality for sums of independent and dependent random vectors. Bull Pol Acad Sci Math 61:155–160
Wang X, Wu Y, Hu S (2016) Exponential probability inequality for \(m\)-END random variables and its applications. Metrika 79(2):127–147
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The authors would like to express their very great appreciation to reviewers for their valuable comments and suggestions which have helped to improve the quality and presentation of this paper
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Naderi, H., Matuła, P. & Amini, M. On Complete Convergence of Dominated Random Variables. Iran J Sci Technol Trans Sci 43, 1161–1165 (2019). https://doi.org/10.1007/s40995-018-0570-4
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DOI: https://doi.org/10.1007/s40995-018-0570-4