DOI QR코드

DOI QR Code

ON CONVERGENCES FOR ARRAYS OF ROWWISE PAIRWISE NEGATIVELY QUADRANT DEPENDENT RANDOM VARIABLES

  • Ryu, Dae-Hee (Department of Computer Science, ChungWoon University) ;
  • Ryu, Sang-Ryul (Department of Computer Science, ChungWoon University)
  • 투고 : 2011.09.06
  • 심사 : 2011.10.19
  • 발행 : 2012.01.30

초록

Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise and pairwise negatively quadrant dependent random variables with mean zero, {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of weights and {$b_n$, $n{\geq}1$} an increasing sequence of positive integers. In this paper we consider some results concerning complete convergence of ${\sum}_{i=1}^{bn}a_{ni}X_{ni}$.

키워드

참고문헌

  1. Ahmed, S.E., Antonini, R.G. and Volodin, A.(2002) On the rate convergence for weighted sums of arrays of Banach valued random elements with application to moving average processes, Statist. Probab. Lett. 58 185-194 https://doi.org/10.1016/S0167-7152(02)00126-8
  2. Bai, Z. and Su, C.(1985) The complete convergence for partial sums of i.i.d. random variables, Sci. Sinica. A28 1261-1277
  3. Baum, L.E. and Katz, M.(1965) Convergence rates in the law of large numbers, Trans. Amer. Soc. 120 108-123 https://doi.org/10.1090/S0002-9947-1965-0198524-1
  4. Chow, Y.S.(1973) Delayed sums and Borel summability of independent identically distributed random variables, Bull. Inst. Math. Acad. Sinica 1 (2) 207-220
  5. Gut, A.(1992) Complete convergence for arrays, Period. Math. Hungar. 25 51-75 https://doi.org/10.1007/BF02454383
  6. Gut, A.(1993) Complete convergence and Cesaro summation for i.i.d. random variables, Probab. Theory Related. Field. 97 169-178 https://doi.org/10.1007/BF01199318
  7. Hsu, P.L. and Robbins, H.(1947) Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 25-31 https://doi.org/10.1073/pnas.33.2.25
  8. Hu, T.C., Li, D., Rosalsky, A. and Volodin, A.(2001) On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements, Theorey Probab. Appl. 47 455-468
  9. Joag-Dev, K. and Proschan, F.(1983) Negative association of random variables with applications, Ann. Statist. 11 286-295 https://doi.org/10.1214/aos/1176346079
  10. Kuczmaszewska, A.(2009)On complete convergence for arrays of rowwise negatively associated random variables, Statist. Probab. Lett. 79 116-124 https://doi.org/10.1016/j.spl.2008.07.030
  11. Lehmann, E.L.(1966) Some concepts of dependence, Ann. Math. Statist. 37 1137-1153 https://doi.org/10.1214/aoms/1177699260
  12. Li, D.L, Rao, M.B., Jiang, T.F. and Wang, X.C.(1995) Complete convergence and almost sure convergence of weighted sums of random variables, J. Theoret. Probab. 8 49-76 https://doi.org/10.1007/BF02213454
  13. Li, D., Rao, M.B. and Wang, X.C.(1992) Complete convergence of moving average processes, Statist. Probab. Lett. 14 111-114 https://doi.org/10.1016/0167-7152(92)90073-E
  14. Liang, H.Y. and Su, C.(1999) Complete convergence for weighted sums of NA sequences, Statist. Probab. Lett. 45 85-95 https://doi.org/10.1016/S0167-7152(99)00046-2
  15. Liang, H.Y.(2000) Complete convergence for weighted sums of negatively associated random variables, Statist. Probab. Lett. 48 317-325 https://doi.org/10.1016/S0167-7152(00)00002-X
  16. Meng, Y. and Lin, Z.(2009) On the weak laws of large numbers for arrays of random variables, Statist. Probab. Lett. 79 2405-2414 https://doi.org/10.1016/j.spl.2009.08.014
  17. Wu, Q.(2006) Probability Limit Theory for Mixing Sequences, Science Press, Beijing China. pp 170-176, 206-211