Lr Convergence for Arrays of Rowwise Negatively Superadditive Dependent Random Variables

doi:10.13371/j.cnki.chin.q.j.m.2016.02.007

Chinese Quarterly Journal of Mathematics ›› 2016, Vol. 31 ›› Issue (2): 162-170.doi: 10.13371/j.cnki.chin.q.j.m.2016.02.007

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L_r Convergence for Arrays of Rowwise Negatively Superadditive Dependent Random Variables

School of Mathematical Sciences,Anhui University

Received:2014-04-18 Online:2016-06-30 Published:2020-11-06
About author:ZHU Hua-yan(1994-), male, native of Hefei, Anhui, engages in probability limit theorem; SHEN Ai-ting(1979-), female, native of Hefei, Anhui, an associate professor of Anhui Universiry, Ph.D., engages in probability limit theorem; ZHANG Ying(1993-), female, native of Putian, Fujian, engages in probability limit theorem.
Supported by:
Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2015A018)； Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)； Supported by the Students Innovative Training Project of Anhui University(201410357118)； Supported by the Quality Engineering Project of Anhui Province(2015jyxm045)； Supported by the Quality Improvement Project for Undergraduate Education of Anhui University(ZLTS2015035)；

Abstract

Abstract: Let {X_nk, k ≥ 1, n ≥ 1} be an array of rowwise negatively superadditive dependent random variables and {a_n, n ≥ 1} be a sequence of positive real numbers such that a_n↑∞. Under some suitable conditions,L_r convergence of 1/a_n max 1≤j≤n |j∑k=1 X_nk| is studied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.

Key words: L_r convergence, convergence in probability, negatively superadditive dependent random variables

CLC Number:

O211.4

ZHU Hua-yan, SHEN Ai-ting, ZHANG Ying. L_r Convergence for Arrays of Rowwise Negatively Superadditive Dependent Random Variables[J]. Chinese Quarterly Journal of Mathematics, 2016, 31(2): 162-170.

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L_r Convergence for Arrays of Rowwise Negatively Superadditive Dependent Random Variables

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