DOI QR코드

DOI QR Code

ON THE MARCINKIEWICZ ZYGMUND LAWS OF LARGE NUMBERS FOR NEGATIVELY DEPENDENT RANDOM FIELDS

  • Ko, Mi-Hwa (Department of Mathematics, WonKwang University)
  • Received : 2011.03.03
  • Accepted : 2011.03.15
  • Published : 2011.06.25

Abstract

In this paper we provide extensions of the Marcinkiewicz Zygmund laws of large numbers for i.i.d random variables with multidimensional indices to the case of negatively dependent random fields.

Keywords

References

  1. Etemati, N.(1981) An elementary proof of the strong law of large numbers, Z. Wahrsch. Verw. Gebiete 55 119-122 https://doi.org/10.1007/BF01013465
  2. Gabriel, J-P.(1977) An inequality for sums of independent random variables indexed by finite dimensional filtering sets and applications to the convergence of series, Ann. Probab. 5 779-786 https://doi.org/10.1214/aop/1176995719
  3. Gut, A.(1978) Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6 469-482 https://doi.org/10.1214/aop/1176995531
  4. Gut, A.(1980) Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices, Ann. Probab. 8 298-313 https://doi.org/10.1214/aop/1176994778
  5. Gut, A. and Spataru, A.(2003) Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables, J. Multi. Anal. 86 398-442 https://doi.org/10.1016/S0047-259X(03)00050-2
  6. Hardy, G.H. and E.M. Wright(1954) An Introduction to the Theory of Numbers, 3rd Edition, Oxford University Press, Oxford
  7. Joag-Dev, K. and F. Proschan(1983) Negative association of random variables with applications, Ann. Statist. 11 286-295 https://doi.org/10.1214/aos/1176346079
  8. Ko, M.H.(2011) On the complete convergence for negatively associated random fields, Taiwan J. Math. 15 171-179 https://doi.org/10.11650/twjm/1500406168
  9. Lehmann, E.L.(1966) Some concepts of dependence, Ann. Math. Statist. 37 1137-1153 https://doi.org/10.1214/aoms/1177699260
  10. Matula, P.(1992) A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15 209-213 https://doi.org/10.1016/0167-7152(92)90191-7
  11. Moore, C.N.(1966) Summable Series and Convergence Factors, Dover, New York
  12. Titchmarsh, E.C.(1951) The Theorey of the Rieman Zeta-Function, Oxford University Press, Oxford