Convergence rates in the law of large numbers for long-range dependent linear processes

被引：4
作者：
Zhang, Tao [1 ]
Chen, Pingyan [2 ]
Sung, Soo Hak [3 ]
机构：
[1] Jinan Univ, Dept Stat, Guangzhou 510630, Guangdong, Peoples R China
[2] Jinan Univ, Dept Math, Guangzhou 510630, Guangdong, Peoples R China
[3] Pai Chai Univ, Dept Appl Math, Daejeon 35345, South Korea
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年
基金：
中国国家自然科学基金; 新加坡国家研究基金会;
关键词：
linear process; convergence rate; Marcinkiewicz-Zygmund law of large numbers; INDEPENDENT RANDOM-VARIABLES; MOVING AVERAGE PROCESSES; LARGE DEVIATIONS; SUMS;
D O I：
10.1186/s13660-017-1517-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Baum and Katz (Trans. Am. Math. Soc. 120: 108-123, 1965) obtained convergence rates in the Marcinkiewicz-Zygmund law of large numbers. Their result has already been extended to the short-range dependent linear processes by many authors. In this paper, we extend the result of Baum and Katz to the long-range dependent linear processes. As a corollary, we obtain convergence rates in the Marcinkiewicz-Zygmund law of large numbers for short-range dependent linear processes.
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页数：14
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