Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

STRONG LAWS FOR WEIGHTED SUMS OF I.I.D. RANDOM VARIABLES (II)

  • Sung, Soo-Hak (Department of Applied Mathematics, Pai Chai University)
  • Published : 2002.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let (X, $X_{n}$, n$\geq$1) be a sequence of i.i.d. random variables and { $a_{ni}$ , 1$\leq$i$\leq$n, n$\geq$1} be an array of constants. Let ø($\chi$) be a positive increasing function on (0, $\infty$) satisfying ø($\chi$) ↑ $\infty$ and ø(C$\chi$) = O(ø($\chi$)) for any C > 0. When EX = 0 and E[ø(｜X｜)]〈$\infty$, some conditions on ø and { $a_{ni}$ } are given under which (equation omitted).).

Keywords

References

  1. Statist. Probab. Lett. v.46 Marcinkiewicz strong laws for linear statistics Z. D. Bai;P. E. Cheng https://doi.org/10.1016/S0167-7152(99)00093-0
  2. Stochastic Anal. Appl. v.5 Almost sure sonvergence theorems of weighted sums of random variables B. D. Choi;S. H. Sung https://doi.org/10.1080/07362998708809124
  3. J. Theoret. Probab. v.8 A strong law for weighted sums of i.i.d. random variables J. Cyzick https://doi.org/10.1007/BF02218047
  4. J. Theoret. Probab. v.8 Complete convergence and almost sure convergence of weighted sums of random variables D. Li;M. B. Rao;T. Jiang;X. Wang https://doi.org/10.1007/BF02213454
  5. Statist. Probab. Lett. v.40 On the limiting behavior of randomly weighted partial sums A. Rosalsky;M. Sreehari https://doi.org/10.1016/S0167-7152(98)00153-9
  6. Almost Sure Convergence W. F. Stout
  7. Statist. Probab. Lett. v.52 Strong laws for weighted sums of i.i.d. random variables S. H. Sung https://doi.org/10.1016/S0167-7152(01)00020-7
  8. Statist. Probab. Lett. v.44 On the strong cenvergence of a weigthed sum W. B. Wu https://doi.org/10.1016/S0167-7152(98)00287-9

Cited by

  1. A Model-Free Measure of Aggregate Idiosyncratic Volatility and the Prediction of Market Returns vol.49, pp.5-6, 2014, https://doi.org/10.1017/S0022109014000489
  2. Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence vol.2012, 2012, https://doi.org/10.1155/2012/562838