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- Title
Almost sure local central limit theorem for the product of some partial sums of negatively associated sequences.
- Authors
Xu, Feng; Wang, Binhui; Hou, Yawen
- Abstract
The almost sure local central limit theorem is a general result which contains the almost sure global central limit theorem. Let { X k , 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 (∏ i = 1 k S k , i / ((k − 1) k μ k)) μ / (σ k) , where E X 1 = μ , σ 2 = E (X 1 − μ) 2 + 2 ∑ k = 2 ∞ E (X 1 − μ) (X k − μ) , S k , i = ∑ j = 1 k X j − X i .
- Subjects
CENTRAL limit theorem; RANDOM variables
- Publication
Journal of Inequalities & Applications, 2019, Vol 2019, Issue 1, pN.PAG
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-019-2261-x