JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (1): 5-11.doi: 10.6040/j.issn.1671-9352.0.2018.449

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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

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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.

Key words: extended negatively dependent random variables, complete moment convergence, complete integral convergence

CLC Number: 

  • O211.4
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