L 1-Convergence for Weighted Sums of Some Dependent Random Variables |
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| Authors: | Pingyan Chen Andrei Volodin |
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| Affiliation: | 1. Department of Mathematics , Jinan University , Guangzhou, P. R. China;2. School of Mathematics and Statistics (M019) , University of Western Australia , Crawley, Western Australia, Australia |
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| Abstract: | In this article, the authors discuss the L 1-convergence for weighted sums of some dependent random variables under the condition of h-integrability with respect to an array of weights. The dependence structure of the random variables includes pairwise lower case negative dependence and conditions on the mixing coefficient, the maximal correlation coefficient, or the ρ*-mixing coefficient. They prove that all the weighted sums have similar limiting behaviour. |
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| Keywords: | Cesàro uniform integrability h-integrability L 1-convergence maximal correlation coefficient Mixing coefficient Pairwise lower case negatively dependent random variables ρ*-mixing coefficient |
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