Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

THE CONVERGENCE RATES IN THE ASYMMETRIC LAWS OF LARGE NUMBER FOR NEGATIVELY ASSOCIATED RANDOM FIELDS

  • Ko, Mi-Hwa (Department of Mathematics, WonKwang University)
  • Received : 2012.02.27
  • Accepted : 2012.03.14
  • Published : 2012.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

Convergence rates in the law of large numbers for i.i.d. random variables have been generalized by Gut[Gut, A., 1978. Marc inkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6, 469-482] to random fields with all indices having the same power in the normalization. In this paper we generalize these convergence rates to the identically distributed and negatively associated random fields with different indices having different power in the normalization.

Keywords

References

  1. 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
  2. Gut, A. and Stadtmuller, U.(2009) An asymmetric Marcinkiewicz - Zygmund LLN for random fields, Statist. Probab. Lett. 79 1016-1020 https://doi.org/10.1016/j.spl.2008.12.006
  3. 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
  4. 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
  5. Li, G.(1994) Multidimensional Levy inequalities and their applications, Probab. Lett. 20 327-335 https://doi.org/10.1016/0167-7152(94)90021-3
  6. Paranjape, S.R. and Park, C.(1973) Laws of iterated logarithm of multiparameter Wiener processes, J. Multivariate Anal. 3 132-136 https://doi.org/10.1016/0047-259X(73)90017-1
  7. Stadtmuller, U. and Thalmaier, M.(2008) Strong laws for delayed sums of random fields, preprint, University of Ulm.