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Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, P. R. China

    De Mei Yuan & Jun An

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  1. De Mei Yuan
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  2. Jun An
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Correspondence to De Mei Yuan.

Additional information

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)

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Yuan, D.M., An, J. Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI. Acta. Math. Sin.-English Ser. 28, 1103–1118 (2012). https://doi.org/10.1007/s10114-012-0033-3

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  • DOI: https://doi.org/10.1007/s10114-012-0033-3

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