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

• Published : 2002.11.01
• 50 4

#### 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

strong laws of large numbers;almost sure convergence;weighted sums of i.i.d. random variables;arrays

#### References

1. 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
2. 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
3. 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
4. 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
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. 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
7. Almost Sure Convergence W. F. Stout
8. 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

#### 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