A note on the almost sure central limit theorem for negatively associated fields

2008 ◽  
Vol 78 (13) ◽  
pp. 1964-1970 ◽  
Author(s):  
Jiang-Feng Wang ◽  
Han-Ying Liang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Negatively Associated

scholarly journals Almost sure local central limit theorem for the product of some partial sums of negatively associated sequences

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Feng Xu ◽  
Binhui Wang ◽  
Yawen Hou
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
General Result ◽  
Random Variables ◽  
Partial Sums ◽  
Negatively Associated ◽  
Associated Sequences ◽  
Local Central Limit Theorem

AbstractThe almost sure local central limit theorem is a general result which contains the almost sure global central limit theorem. Let $\{X_{k},k\geq 1\}${Xk,k≥1} be a strictly stationary negatively associated sequence of positive random variables. Under the regular conditions, we discuss an almost sure local central limit theorem for the product of some partial sums $(\prod_{i=1}^{k} S_{k,i}/((k-1)^{k}\mu^{k}))^{\mu/(\sigma\sqrt{k})}$(∏i=1kSk,i/((k−1)kμk))μ/(σk), where $\mathbb{E}X_{1}=\mu$EX1=μ, $\sigma^{2}={\mathbb{E}(X_{1}-\mu)^{2}}+2\sum_{k=2}^{\infty}\mathbb{E}(X_{1}-\mu)(X_{k}-\mu)$σ2=E(X1−μ)2+2∑k=2∞E(X1−μ)(Xk−μ), $S_{k,i}=\sum_{j=1}^{k}X_{j}-X_{i}$Sk,i=∑j=1kXj−Xi.

scholarly journals The Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yuanying Jiang ◽  
Qunying Wu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Associated Sequences ◽  
Local Central Limit Theorem

In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables:limn→∞(1/logn)∑k=1n(I(ak≤Sk<bk)/k)P(ak≤Sk<bk)=1, almost surely. This is the local almost sure central limit theorem for negatively associated sequences similar to results by Csáki et al. (1993). The results extend those on almost sure local central limit theorems from the i.i.d. case to the stationary negatively associated sequences.

scholarly journals Almost sure central limit theorem for self-normalized partial sums of negatively associated random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1413-1422 ◽  
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Stationary Sequence ◽  
The Self ◽  
Partial Sums ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables

Let X,X1,X2,... be a stationary sequence of negatively associated random variables. A universal result in almost sure central limit theorem for the self-normalized partial sums Sn/Vn is established, where: Sn = ?ni=1 Xi,V2n = ?ni=1 X2i .

Sign in / Sign up

Export Citation Format

Share Document