《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (1): 5-11.

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### END随机变量的完全矩收敛和完全积分收敛

1. 安徽大学数学科学学院, 安徽 合肥 230601
• 发布日期:2020-01-10
• 作者简介:张雅静(1991— ),女,硕士研究生,研究方向为概率极限理论. E-mail:418012236@qq.com*通信作者简介:沈爱婷(1979— ),女,博士,博士生导师,研究方向为概率极限理论. E-mail:empress201010@126.com
• 基金资助:
国家自然科学基金资助项目(11501004);安徽高校省级自然科学基金重点项目(KJ2015A018)

### Complete moment convergence and complete integral convergence for END random variables

ZHANG Ya-jing, TAO Hui-ling, LI Xiang, SHEN Ai-ting*

1. School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
• Published:2020-01-10

Abstract: Let {X,Xn,n≥1} be a sequence of extended negatively dependent(END)random variables with identical distribution, and Sn=∑ni=1Xi, n≥1. The equivalent conditions between complete moment convergence n=1nr-2-1/(pq)anE(max1≤k≤n|Sk|1/q-εbn1/(pq))+<∞, ∠ε>0and complete integral convergence were investigated under two cases: r>1, q>0, 02, an=1, bn=n and p=2, an=(log n)-1/(2q), bn=n log n. The results obtained generalize the corresponding ones for negatively associated(NA)random variables and negatively orthant dependent(NOD)random variables.

• O211.4
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