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.

引用

页数：14

共 50 条

[21] Wavelet Estimator of Long-Range Dependent Processes
J. M. Bardet
G. Lang
E. Moulines
P. Soulier
Statistical Inference for Stochastic Processes, 2000, 3 (1-2) : 85 - 99
[22] Convergence of Sample Autocorrelation of Long-Range Dependent Traffic
Li, Ming
Zhao, Wei
MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
[23] A regularised estimator for long-range dependent processes
Vivero, Oskar
Heath, William P.
AUTOMATICA, 2012, 48 (02) : 287 - 296
[24] CONVERGENCE-RATES RELATED TO THE STRONG LAW OF LARGE NUMBERS
FILL, JA
ANNALS OF PROBABILITY, 1983, 11 (01): : 123 - 142
[25] A PAIR OF COMPLEMENTARY THEOREMS ON CONVERGENCE RATES IN LAW OF LARGE NUMBERS
HEYDE, CC
ROHATGI, VK
PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1967, 63 : 73 - &
[26] Rates of convergence for the Nummelin conditional weak law of large numbers
Kuelbs, J
Meda, A
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 98 (02) : 229 - 252
[27] Convergence rates in the law of large numbers for arrays of martingale differences
Hao, Shunli
Liu, Quansheng
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 417 (02) : 733 - 773
[28] On Convergence Rates in the Marcinkiewicz–Zygmund Strong Law of Large Numbers
Fakhreddine Boukhari
Results in Mathematics, 2021, 76
[29] Convergence rates in the law of large numbers and new kinds of convergence of random variables
Hu, Ze-Chun
Sun, Wei
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2021, 50 (18) : 4308 - 4323
[30] RATES OF CONVERGENCE AND OPTIMAL SPECTRAL BANDWIDTH FOR LONG-RANGE DEPENDENCE
ROBINSON, PM
PROBABILITY THEORY AND RELATED FIELDS, 1994, 99 (03) : 443 - 473

← 1 2 3 4 5 →