Abstract
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.
Highlights
The almost sure central limit theorem is established for sequences of negatively associated random variables: limn → ∞(1/ log n) ∑nk=1(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 Csaki 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
Summary
The almost sure central limit theorem is established for sequences of negatively associated random variables: limn → ∞(1/ log n) ∑nk=1(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 Csaki 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.
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