| Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI |
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| 基金项目： | Supported by National Natural Science Foundation of China （Grant No. 10871217）, Natural Science Foundation Project of CQ CSTC of China （Grant No. 2009BB2370） and SCR of Chongqing Municipal Education Commission （Grant Nos. KJ090703, KJ100726）Acknowledgements The authors would like to thank the anonymous referees sincerely for their valuable comments and suggestions on a previous draft, which resulted in the present version of this paper. |
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| 摘 要： | Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.
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| 关 键 词： | Law of large numbers residual Cesàro alpha-integrability strong residual Cesàro alpha-integrability asymptotically almost negative association asymptotically quadrant sub-independence |
Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI |
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| Authors: | De Mei Yuan Jun An |
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| Institution: | 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, P. R. China
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| Abstract: | Both residual Cesàro alpha-integrability (RCI(α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymptotically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L 1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature. |
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| Keywords: | Law of large numbers residual Cesaro alpha-integrability strong residual Cesaro alphaintegrability asymptotically almost negative association asymptotically quadrant sub-independence |
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