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Applied Mathematics-A Journal of Chinese Universities  2018, Vol. 33 Issue (1): 35-47    DOI: 10.1007/s11766-018-3423-1
    
On the strong convergence properties for weighted sums of negatively orthant dependent random variables
DENG Xin, TANG Xu-fei, WANG Shi-jie, WANG Xue-jun
School of Mathematical Sciences, Anhui University, Hefei 230601, China
On the strong convergence properties for weighted sums of negatively orthant dependent random variables
DENG Xin, TANG Xu-fei, WANG Shi-jie, WANG Xue-jun
School of Mathematical Sciences, Anhui University, Hefei 230601, China
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摘要: In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent (NOD) random variables are investigated. Let $\{X_n, n\geq1\}$ be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable $X$. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.
关键词: strong convergencenegatively orthant dependent random variablesstochastic domination    
Abstract: In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent (NOD) random variables are investigated. Let $\{X_n, n\geq1\}$ be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable $X$. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.
Key words: strong convergence    negatively orthant dependent random variables    stochastic domination
收稿日期: 2015-12-02 出版日期: 2018-03-28
CLC:  60F15  
基金资助: Supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005), the Quality Engineering Project of Anhui Province (2016jyxm0047) and the Graduate Academic Innovation Research Project of Anhui University (yfc100004).
通讯作者: WANG Xue-jun     E-mail: wxjahdx@126.com
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引用本文:

DENG Xin, TANG Xu-fei, WANG Shi-jie, WANG Xue-jun. On the strong convergence properties for weighted sums of negatively orthant dependent random variables[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 35-47.

DENG Xin, TANG Xu-fei, WANG Shi-jie, WANG Xue-jun. On the strong convergence properties for weighted sums of negatively orthant dependent random variables. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 35-47.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-018-3423-1        http://www.zjujournals.com/amjcub/CN/Y2018/V33/I1/35

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