호남수학학술지 (Honam Mathematical Journal)

  • 제36권4호
  • /
  • Pages.767-775
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  • 2014
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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ON CONDITIONAL BOREL-CANTELLI LEMMA UNDER PAIRWISE EXTENDED CONDITIONAL NEGATIVE QUADRANT DEPENDENCE

  • 투고 : 2014.08.25
  • 심사 : 2014.09.02
  • 발행 : 2014.12.25
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초록

In this paper we define the extended conditional negative quadrant dependence and generalize the conditional Borel-Cantelli lemma of B.L.S. Prakasa Rao(2012) to the case of pairwise extended conditionally negative quadrant dependence.

키워드

참고문헌

  1. Chung, K.L. and Erdos, P., On the application of the Borel-Cantelli lemma, Trans. Amer. Math. Soc. 72 (1952), 179-186. https://doi.org/10.1090/S0002-9947-1952-0045327-5
  2. 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
  3. Erdos, P. and Renyi, A., On cantor's series with convergent ${\sum}\frac{1}{q}$, Ann. Univ. Sci. Poudapest Sect. Math. 2 (1959), 93-109.
  4. Lehmann. E.L., Some concepts of dependence, Ann. Math. Stat. 37 (1966), 1137-1153. https://doi.org/10.1214/aoms/1177699260
  5. Majerak, D., Newak, W. and Zieba, W., Conditional strong law of large number, Inter. J. Pure. Appl. Math. 20 (2005), 143-157.
  6. 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
  7. B.L.S. Prakasa Rao, Conditional independence, conditional mixing and conditional association, Ann. Statist. Math. 61 (2009), 441-460. https://doi.org/10.1007/s10463-007-0152-2
  8. B.L.S. Prakasa Rao, Upper and lower bounds for probabilities in the conditinal Borel-Cantelli lemma, Stoch. Anal. Appl. 28 (2010), 144-156.

피인용 문헌

  1. On inequalities for conditional probabilities of unions of events and the conditional Borel–Cantelli lemma vol.49, pp.4, 2016, https://doi.org/10.3103/S1063454116040063