Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI  

作　　者：De Mei YUAN Jun AN 

机构地区：[1]School of Mathematics and Statistics,Chongqing Technology and Business University

出　　处：《Acta Mathematica Sinica,English Series》2012年第6期1103-1118,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10871217);Natural Science Foundation Project of CQ CSTC of China (Grant No. 2009BB2370);SCR of Chongqing Municipal Education Commission (Grant Nos. KJ090703, KJ100726)

摘　　要：Both residual Cesaro alpha-integrability （RCI（α） and strongly residual Cesaro 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 Ll-convergence results and the SRCI（α） property yields strong laws of large numbers, which is the continuation of the corresponding literature.Both residual Cesaro alpha-integrability （RCI（α） and strongly residual Cesaro 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 Ll-convergence results and the SRCI（α） property yields strong laws of large numbers, which is the continuation of the corresponding literature.

关 键 词：Law of large numbers residual Cesaro alpha-integrability strong residual Cesaro alphaintegrability asymptotically almost negative association asymptotically quadrant sub-independence 

分 类 号：O211.5[理学—概率论与数理统计]