Complete Moment and Integral Convergence for Sums of Negatively Associated Random Variables
Complete Moment and Integral Convergence for Sums of Negatively Associated Random Variables
复制标题
负相关随机变量之和的完全矩和积分收敛
DOI：
10.1007/s10114-010-8177-5
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发表时间：
2010-03-01
影响因子：
0.7
通讯作者：
Rosalsky, Andrew
中科院分区：
文献类型：
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作者：
Liang, Han Ying;Li, De Li;Rosalsky, Andrew
对具有部分和S-n = Sigma（n）（i=1）X-i，n >= 1的同分布负相协随机变量序列{X-n; n >= 1}，给出了经典Baum-Katz和Lai完全收敛定理的改进.更具体地说，给出了如下形式的矩完全收敛的充要条件：Sigma（n ≥ n 0）n（r-2-1/pq）alpha（n）E（max（1 0）且n（0）= 1，0 < p < 2，a（n）= 1，B（n）= n或n（0）= 3，p = 2，a（n）=（log n）（-1.2q），B（n）= nlog n.这些结果将Chow和Li和Spataru的结果从独立同分布的情形推广到同分布的负相关情形。证明了完全矩收敛等价于完全积分收敛。
For a sequence of identically distributed negatively associated random variables {X-n; n >= 1} with partial sums S-n = Sigma(n)(i=1) X-i, n >= 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the formSigma(n >= n0) n(r-2-1/pq) alpha(n) E (max(1 0 and either n(0) = 1, 0 < p < 2, a(n) = 1, b(n) = n or n(0) = 3, p = 2, a(n) = (log n)(-1.2q), b(n) = n log n. These results extend results of Chow and of Li and Spataru from the independent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.