Hilbert空间中φ-混合随机元序列的大数定律(英文)  

LAWS OF LARGE NUMBERS FOR SEQUENCES OF φ-MIXING RANDOM ELEMENTS IN HILBERT SPACE

作　　者：安军[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《数学杂志》2013年第6期1027-1035,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10871217);Projects of Science and Technology Research of Chongqing City Education Committee(KJ1307XX)

摘　　要：本文研究可分Hilbert空间中的φ-混合随机元序列的收敛性.利用截尾法和Borel-Cantelli引理、Kronecker引理等工具,在某种Chung型条件下,得到了弱大数定律和Marcinkiewicz-Zygmund型强大数定律,推广了实值随机变量序列的已知结果.In this paper, we study the convergence for sequences of φ-mixing random elements in separable Hilbert space. Applying the method of truncation and the tools of Broel-Cantelli lemma and Kronecker lemma, we obtain the weak law of large numbers under some Chung type conditions, and establish the Marcinkiewicz-Zygmund type strong law of large numbers, which extend some known ones for sequences of real-valued random variables.

关 键 词：φ-混合随机元 可分Hilbert空间 大数定律 

分 类 号：O211.4[理学—概率论与数理统计]