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

被引：3

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：

新加坡国家研究基金会; 中国国家自然科学基金;

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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