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Applied Mathematics-A Journal of Chinese Universities  2020, Vol. 35 Issue (2): 184-192    DOI: 10.1007/s11766-020-3480-0
    
On the convergence for PNQD sequences with general moment conditions
XIAO Juan, QIU De-hua
1School of Mathematics and Statistics, Hengyang Normal University, Hengyang 421008, China.
2School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China.
On the convergence for PNQD sequences with general moment conditions
XIAO Juan, QIU De-hua
1School of Mathematics and Statistics, Hengyang Normal University, Hengyang 421008, China.
2School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China.
 全文: PDF 
摘要：  Let {X, Xn, n ≥ 1} be a sequence of identically distributed pairwise negative quadrant dependent (PNQD) random variables and {an, n ≥ 1} be a sequence of positive constants with an = f(n) and f(θk)/f(θk?1) ≥ β for all large positive integers k, where 1 < θ ≤ β and
f(x) > 0 (x ≥ 1) is a non-decreasing function on [b, +∞) for some b ≥ 1. In this paper, we obtain the strong law of large numbers and complete convergence for the sequence {X, Xn, n ≥ 1},which are equivalent to the general moment condition ∑∞n=1 P(|X| > an) < ∞. Our results extend and improve the related known works in Baum and Katz [1], Chen at al. [3], and Sung[14].
关键词： pairwise negative quadrant dependent (PNQD) random variable;  strong law of large numbers;  complete convergence;  general moment condition    
Abstract:  Let {X, Xn, n ≥ 1} be a sequence of identically distributed pairwise negative quadrant dependent (PNQD) random variables and {an, n ≥ 1} be a sequence of positive constants with an = f(n) and f(θk)/f(θk?1) ≥ β for all large positive integers k, where 1 < θ ≤ β and
f(x) > 0 (x ≥ 1) is a non-decreasing function on [b, +∞) for some b ≥ 1. In this paper, we obtain the strong law of large numbers and complete convergence for the sequence {X, Xn, n ≥ 1},which are equivalent to the general moment condition ∑∞n=1 P(|X| > an) < ∞. Our results extend and improve the related known works in Baum and Katz [1], Chen at al. [3], and Sung[14].
Key words: pairwise negative quadrant dependent (PNQD) random variable    strong law of large numbers    complete convergence    general moment condition
出版日期: 2020-06-01
CLC:  60F15  
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引用本文:

XIAO Juan, QIU De-hua. On the convergence for PNQD sequences with general moment conditions[J]. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 184-192.

XIAO Juan, QIU De-hua. On the convergence for PNQD sequences with general moment conditions. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 184-192.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-020-3480-0    或    http://www.zjujournals.com/amjcub/CN/Y2020/V35/I2/184

[1] HUANG Jian-wen, WANG Jian-jun. Higher order asymptotic behaviour of partial maxima of random sample from generalized Maxwell distribution under power normalization[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 177-.
[2] 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.