ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF φ-MIXING RANDOM VARIABLES

被引：11

作者：

Huang, Haiwu ^{[1
,2
]}

Wang, Dingcheng ^{[3
]}

Peng, Jiangyan ^{[4
]}

机构：

[1] Guangxi Sci Expt Ctr Min Met & Environm, Guilin 541004, Peoples R China

[2] Guilin Univ Technol, Coll Sci, Guilin 541004, Peoples R China

[3] Nanjing Audit Univ, Ctr Financial Engn, Nanjing 211815, Jiangsu, Peoples R China

[4] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 610054, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2014年 / 8卷 / 03期

基金：

中国国家自然科学基金;

关键词：

phi-mixing random variables; strong law of large numbers; weighted sums; MOVING AVERAGE PROCESSES; CENTRAL-LIMIT-THEOREM; INVARIANCE-PRINCIPLE;

D O I：

10.7153/jmi-08-34

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let {X-n, n >= 1} be a sequence of phi-mixing random variables with non-identical distribution and {a(ni);1 <= i <= n, n >= 1} be an array of real constants. In this paper, we study the strong law of large numbers for the maximal weighted sums of phi-mixing random variables. The results obtained generalize and improve the previous known result of Bai and Cheng (Z.D. Bai and P.E. Cheng, 2000. Marcinkiewicz strong laws for linear statistics. Statist. Probab. Lett. vol. 46, no. 2, pp. 105-112.) for independent and identically distributed random variables to phi-mixing case.

引用

页码：465 / 473

页数：9

共 14 条

[1] Marcinkiewicz strong laws for linear statistics [J].

Bai, ZD ;

Cheng, PE .

STATISTICS & PROBABILITY LETTERS, 2000, 46 (02) :105-112

[2] A UNIFORM CENTRAL-LIMIT-THEOREM FOR NONUNIFORM PHI-MIXING RANDOM-FIELDS [J].

CHEN, DC .

ANNALS OF PROBABILITY, 1991, 19 (02) :636-649

[3] Limiting behaviour of moving average processes under φ-mixing assumption [J].

Chen, Pingyan ;

Hu, Tien-Chung ;

Volodin, Andrei .

STATISTICS & PROBABILITY LETTERS, 2009, 79 (01) :105-111

[4]

DOBRUSHIN RL, 1956, THEORY PROBAB APPL, V1, P72

[5] THE INVARIANCE-PRINCIPLE FOR PSI-MIXING SEQUENCES [J].

HERRNDORF, N .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1983, 63 (01) :97-108

[6] AN INVARIANCE-PRINCIPLE FOR PHI-MIXING SEQUENCES [J].

PELIGRAD, M .

ANNALS OF PROBABILITY, 1985, 13 (04) :1304-1313

[7] ALMOST SURE INVARIANCE-PRINCIPLES FOR MIXING SEQUENCES OF RANDOM-VARIABLES [J].

SHAO, QM .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1993, 48 (02) :319-334

[8] ON THE CENTRAL-LIMIT-THEOREM FOR RHO-MIXING ARRAYS OF RANDOM-VARIABLES [J].

UTEV, SA .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 1990, 35 (01) :131-139

[9]

Wang XJ, 2012, RACSAM REV R ACAD A, V106, P321, DOI 10.1007/s13398-011-0056-0

[10] On Complete Convergence for Weighted Sums of φ-Mixing Random Variables [J].

Wang Xuejun ;

Hu Shuhe ;

Yang Wenzhi ;

Shen Yan .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,

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