Strong law of large numbers for pair-wise extended lower/upper negatively dependent random variables

Fengyang CHENG

PDF(122 KB)
PDF(122 KB)
Front. Math. China ›› 2014, Vol. 9 ›› Issue (5) : 1019-1031. DOI: 10.1007/s11464-014-0376-4
RESEARCH ARTICLE
RESEARCH ARTICLE

Strong law of large numbers for pair-wise extended lower/upper negatively dependent random variables

Author information +
History +

Abstract

We establish some strong limit theorems for a sequence of pair-wise extended lower/upper negatively dependent random variables and give some new examples of dependent random variables.

Keywords

Extended negatively dependence / strong law of large numbers (SLLN) / weighted sums

Cite this article

Download citation ▾
Fengyang CHENG. Strong law of large numbers for pair-wise extended lower/upper negatively dependent random variables. Front. Math. China, 2014, 9(5): 1019‒1031 https://doi.org/10.1007/s11464-014-0376-4

References

[1]
Block H W, Savits T H, Shaked M. Some concepts of negative dependence. Ann Probab, 1982, 10: 765-772
CrossRef Google scholar
[2]
Chen Y, Chen A Y, Ng K W. The strong law of large numbers for extended negatively dependent random variables. J Appl Probab, 2010, 47: 908-922
CrossRef Google scholar
[3]
Chen Y, Yuen K C, Ng K W. Precise large deviations of random sums in presence of negative dependence and consistent variation. Methodol Comput Appl Probab, 2011, 13: 821-833
CrossRef Google scholar
[4]
Cheng F Y, Li N. Asymptotics for the tail probability of random sums with a heavytailed random number and extended negatively dependent summands. Chin Ann Math Ser B, 2014, 35: 69-78
CrossRef Google scholar
[5]
Ebrahimi N, Ghosh M. Multivariate negative dependence. Comm Statist Theory Methods, 1981, 8: 625-641
[6]
Etemadi N. An elementary proof of the strong law of large numbers. Z Wahrsch verw Geb, 1981, 55: 119-122
[7]
Etemadi N. Stability of sums weighted nonnegative random variables. J Multivariate Anal, 1983, 13: 361-365
CrossRef Google scholar
[8]
Lehmann E L. Some concepts of dependence. Ann Math Stat, 1966, 37: 1137-1153
CrossRef Google scholar
[9]
Liu L. Precise large deviations for dependent random variables with heavy tails. Statist Probab Lett, 2009, 79: 1290-1298
CrossRef Google scholar
[10]
Wang K, Wang Y, Gao Q. Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate. Methodol Comput Appl Probab, 2013, 15: 109-124
CrossRef Google scholar
[11]
Wang Y, Cheng D. Basic renewal theorems for random walks with widely dependent increments. J Math Anal Appl, 2011, 384: 597-606
CrossRef Google scholar

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
AI Summary AI Mindmap
PDF(122 KB)

Accesses

Citations

Detail

Sections
Recommended

/