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THE BOREL-CANTELLI LEMMA UNDER PAIRWISE EXTENDED NEGATIVE QUADRANT DEPENDENCE

  • Ko, Mi-Hwa (Division of Mathematics and Informational Statistics, WonKwang University)
  • Received : 2013.03.05
  • Accepted : 2013.03.19
  • Published : 2013.06.25

Abstract

By extending the negatively quadrant dependence, the paper puts forth the concept of extended negative quadrant dependence. A generalization of the second Borel-Cantelli lemma is obtained under extended negative quadrant dependence. Some applications are also introduced.

Keywords

References

  1. Block, H.W., Savits, T.H. and Shaked, M., Some concepts of negative dependence, Ann. Probab. 10 (1982), 765-772. https://doi.org/10.1214/aop/1176993784
  2. Chung, K.L. and Erdos, P., On the application of Borel-Cantelli lemma, Trans. Amer. Soc. 72 (1952), 179-186. https://doi.org/10.1090/S0002-9947-1952-0045327-5
  3. Chandra, T.K., The Borel-Cantelli lemma under dependence conditions, Statist. Probab. Lett. 78 (2008), 390-395. https://doi.org/10.1016/j.spl.2007.07.023
  4. Erdos, P. and Renyi, A., On Cantor's series with convergent ${\Sigma}\frac{1}{qn}$, Ann. Univ. Sei. Vudapest. Sect. Math. 2 (1959), 93-109.
  5. Ko, B. and Tang, Q., Sums of dependent nonnegative random variables with subexponential tails, J. Appl. Prob. 45 (2008), 85-94. https://doi.org/10.1239/jap/1208358953
  6. Lehmann, E.L., Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153. https://doi.org/10.1214/aoms/1177699260
  7. Liu, L., Precise large deviations for dependent variables with heavy tails, Statist. Probab. Lett. 79 (2009), 1290-1298. https://doi.org/10.1016/j.spl.2009.02.001
  8. Petrov, V.V., A note on the Borel-Cantelli lemma, Statist. Probab. Lett. 58 (2002), 283-286. https://doi.org/10.1016/S0167-7152(02)00113-X
  9. Petrov, V.V., A generalization of the Borel-Cantelli lemma, Statist. Probab. Lett. 67 (2004), 233-239. https://doi.org/10.1016/j.spl.2004.01.008