General results of complete convergence and complete moment convergence for weighted sums of some class of random variables |
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| Authors: | Xuejun Wang Shuhe Hu Andrei Volodin |
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| Affiliation: | 1. School of Mathematical Science, Anhui University, Hefei, Anhui, P.R. Chinawxjahdx@126.com;3. School of Mathematical Science, Anhui University, Hefei, Anhui, P.R. China;4. Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada |
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| Abstract: | ABSTRACTIn the article, the complete convergence and complete moment convergence for weighted sums of sequences of random variables satisfying a maximal Rosenthal type inequality are studied. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. Our partial results generalize and improve the corresponding ones of Shen (2013 Shen, A.T. (2013). On strong convergence for weighted sums of a class of random variables. Abstr. Appl. Anal.2013, Article ID 216236: 1–7. [Google Scholar]). |
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| Keywords: | Complete convergence Complete moment convergence Rosenthal type maximal inequality Marcinkiewicz–Zygmund type strong law of large numbers |
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