ρ混合阵列的收敛性

Abstract

Abstract:

In this paper the authors introduce the concept of arrays of ρ～ mixing random variables and study the complete convergence and the convergence in probabillity for such arrays of ρ～ mixing random variables. The results extend the corresponding ones of arrays of rowwise independent random variables. In the other direction, the complete convergence and the convergence in probability for arbitrary random variable arrays are obtained.

Key words: ρ～ mixing array, Complete convergence

CLC Number:

60F15

Cite this article

QIU De-Hua, GAN Shi-Shen. Convergence of Arrays of rho Mixing Random Variables[J].Acta mathematica scientia,Series A, 2005, 25(1): 73-78.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbA/EN/

http://121.43.60.238/sxwlxbA/EN/Y2005/V25/I1/73

Trendmd

References

[1]Bradley R C. Equivalent Mixing Conditions for Random Fields. Technical Report No. 336. Center for Stochastic Processes: Univ of North Carolina, 1990

[2]Bradley R C. On the spectral density and asymptotic normality of weakly dependent random fields. J Theoret Probab, 1992, 5:355-374

[3]Bryc W, Smolenski W. Moment conditions for almost sure convergence of weakly correlated random variables. Proceedings of American Math Society, 1993, 119(2):629-635

[4]杨善朝.一类随机变量部分和的矩不等式及其应用. 科学通报，1998， 43(17)：1823-1827

[5]吴群英.p~混合序列加权和的完全收敛性和强收敛性. 应用数学，2002，15(1)：1-4

[6]HU T C, Taylor R L. On the strong law for arrays and for the bootstrap mean and variance. Internat J Math & Math Sci, 1997, 20(2):375-382

[7]Hsu P L, Robbins H. Complete convergence and the strong law of largenumbers. Proc Nat Acad Sci, 1947,33(2): 25-31

[8]Bozorgnia A, Patterson R F, Taylor R L. On strong laws of large numbers for arrays of rowwise independent random elements. Internat J Math & Mat h Sci, 1993, 16(3): 587-592

Related Articles 14

[1]	Li Wei. Complete Convergence for Weighted Sums Under END Setup [J]. Acta mathematica scientia,Series A, 2016, 36(3): 448-455.
[2]	Qiu Dehua, Chen Pingyan. large Convergence for Moving Average Processes Under END Set-up [J]. Acta mathematica scientia,Series A, 2015, 35(4): 756-768.
[3]	Li Wei. Complete Convergence for Sung's Type Weighted Sums Under NOD Setup [J]. Acta mathematica scientia,Series A, 2015, 35(4): 729-737.
[4]	LING Neng-Xiang, DING Jie. Asymptotic Properties of Conditional Density Estimation for Dependence Functional Data [J]. Acta mathematica scientia,Series A, 2012, 32(3): 547-556.
[5]	HU Shu-He, LI Xiao-Qin, YANG Wen-Zhi, WANG Xue-Jun. Bernstein Inequalities and Inverse Moments for Mixing Sequences [J]. Acta mathematica scientia,Series A, 2012, 32(3): 441-449.
[6]	CHEN Ping-Yan, LI Yuan-Mei. Limiting Behavior of Moving Average Processes of Martingale Difference Sequences [J]. Acta mathematica scientia,Series A, 2011, 31(1): 179-187.
[7]	GAN Shi-Xin. Rosenthal's Inequality and Its Applications for B -valued Random Elements [J]. Acta mathematica scientia,Series A, 2010, 30(2): 327-334.
[8]	YAO Qiang. A Proof of the Complete Convergence Theorem for Contact Processes on Some Product Graphs [J]. Acta mathematica scientia,Series A, 2010, 30(1): 97-102.
[9]	Gan Shixin;Chen Pingyan. Strong Convergence Rate of Weighted Sums for NOD Sequences [J]. Acta mathematica scientia,Series A, 2008, 28(2): 283-290.
[10]	Li Yunxia. Precise Asymptotics in the Law of Large Numbers of Moving-average Processes [J]. Acta mathematica scientia,Series A, 2006, 26(5): 675-687.
[11]	WANG Jian-Feng, JIN Jing-Sen. Marcinkiewicz Laws of Large Numbers and Complete Convergence with Multidimensional Indices [J]. Acta mathematica scientia,Series A, 2005, 25(5): 734-743.
[12]	Liang Hanying, Xuc Zhanao, Niu Sili. Complete Convergence and laws of large Numbers for Arrays of B-Valued Random Elements [J]. Acta mathematica scientia,Series A, 1998, 18(1): 89-96.
[13]	Liang Hanying, Niu Sili. Complete Convergence for Sums of B-valued Random Elements [J]. Acta mathematica scientia,Series A, 1997, 17(S1): 76-82.
[14]	Su Chun, Wang Yuebao. A Further Discussion on the Complet Con-Vergence of Randomly Indexed Sums of B-Valued Elements [J]. Acta mathematica scientia,Series A, 1997, 17(1): 74-80.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Shi Shaoyun. Nonexistence and Partial Existence of Rational First Integrals for General Nonlinear Systems[J]. Acta mathematica scientia,Series A, 2008, 28(4): 603 -611 .
[2]	Xin Yongxun;Liu Guizhen. On Super f- Edge Cover-Coloring of Multigraphs[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1164 -1172 .
[3]	Xu Xingye. The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rⁿ[J]. Acta mathematica scientia,Series A, 2009, 29(1): 87 -93 .
[4]	Zhang Feijun; Li Kaitai. The Embedded Subbundles over Module Bundles[J]. Acta mathematica scientia,Series A, 2009, 29(1): 151 -157 .
[5]	Liu Xiaopeng; Liu Kunhui. The Changes of F Distribution Density Curve[J]. Acta mathematica scientia,Series A, 2007, 27(2): 331 -342 .
[6]	Sun Liying. The Satisfactory Improvements of the Modified Gauss-Seidel Method for H -matrices[J]. Acta mathematica scientia,Series A, 2006, 26(4): 591 -594 .
[7]	Jiang Yiwen. Cross-estimate and Tightness for Non-symmetric Markov Processes[J]. Acta mathematica scientia,Series A, 2007, 27(5): 923 -930 .
[8]	Liang Zhiqing;Chen Lansun. Stability of Periodic Solution for a Discrete Leslie Predator-prey System [J]. Acta mathematica scientia,Series A, 2006, 26(4): 634 -640 .
[9]	Tong Xiaojiao;He Bingsheng. An Inexact Alternating Direction Method for Solving a Class of Monotone Variational Inequalities [J]. Acta mathematica scientia,Series A, 2006, 26(2): 273 -282 .
[10]	Lin Lishan;Li Yongqing. Existence of Solutions of Nonlinear Eigenvalue Problems Laplacian and Weights [J]. Acta mathematica scientia,Series A, 2007, 27(6): 996 -1005 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP

Convergence of Arrays of rho Mixing Random Variables

PDF (PC)