Complete Convergence and Complete Moment Convergence for Martingale Diference Sequence  

作　　者：Xue Jun WANG Shu He HU 

机构地区：[1]School of Mathematical Science,Anhui University

出　　处：《Acta Mathematica Sinica,English Series》2014年第1期119-132,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11201001,11171001,11126176 and 11226207);Natural Science Foundation of Anhui Province(Grant Nos.1208085QA03 and 1308085QA03);Applied Teaching Model Curriculum of Anhui University(Grant No.XJYYXKC04);Students Innovative Training Project of Anhui University(Grant No.201310357004);Doctoral Research Start-up Funds Projects of Anhui University and the Students Science Research Training Program of Anhui University(Grant No.KYXL2012007)

摘　　要：In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.

关 键 词：Martingale diference sequence complete convergence complete moment convergence Baum–Katz-type theorem 

分 类 号：O211.6[理学—概率论与数理统计]