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The almost sure local central limit theorem for products of partial sums under negative association

机译：负关联下部分和的乘积的几乎确定的局部中心极限定理

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摘要

Let {Xn, n ≥ 1} be a strictly stationary negatively associated sequence of positive random variables with EX1 = μ 0 and Var(X1) = σ² ∞. Denote

S_{n} = \sum_{i = 1}^{n} X_{i}, p_{k} = P (a_{k} \leq {(\prod_{j = 1}^{k} S_{j} / (k! μ^{k}))}^{1 / (γ σ_{1} \sqrt{k})} < b_{k})

and γ = σ/μ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem

lim_{n \to \infty} \frac{1}{log n} \sum_{k = 1}^{n} \frac{1}{k p_{k}} I {a_{k} \leq {(\frac{\prod_{j = 1}^{k} S_{j}}{k! μ^{k}})}^{1 / (γ σ_{1} \sqrt{k})} < b_{k}} = 1 a.s.,

where

σ_{1}^{2} = 1 + \frac{1}{σ^{2}} \sum_{j = 2}^{\infty} Cov (X_{1}, X_{j}) > 0

机译：假设{Xn，n≥1}是一个具有EX1 =μ> 0且Var（X1）=σ^{2 <∞的正静态变量的严格平稳的负相关序列。表示 $Sn=\sumi=1nXi，pk=P（ak\leq（\prodj=1kSj/（k！μk））1/$}

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期刊名称 Springer Open Choice
作者
Yuanying Jiang; Qunying Wu;
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作者单位

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年(卷),期 -1(2018),1
年度 -1
页码 275
总页数 16
原文格式 PDF
正文语种
中图分类外科学;
关键词
Negative association Products of partial sums Almost sure local central limit theorem Almost sure global central limit theorem;

机译：负关联;部分和的乘积;几乎确定的局部中心极限定理;几乎确定的整体中心极限定理;

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专利

1. The almost sure local central limit theorem for products of partial sums under negative association [J] . Yuanying Jiang, Qunying Wu Journal of inequalities and applications . 2018,第1期

机译：负关联下部分和的乘积的几乎确定的局部中心极限定理
2. An almost sure central limit theorem for products of sums of partial sums under association [J] . Zhang Y., Yang X.-Y., Dong Z.-S. Journal of Mathematical Analysis and Applications . 2009,第2期

机译：关联下部分和的乘积的几乎确定的中心极限定理
3. Almost sure central limit theorem for self-normalized products of partial sums of negatively associated sequences [J] . Wu Qunying Communications in Statistics . 2017,第5a6期

机译：几乎肯定的中央限位定理，适用于消极相关序列的部分和的自标准化产品
4. Limit theorems for the partial sum in Engel continued fractions [C] . Zhiyong Wang, Ruibiao Zou, Dongdong Zhu International Conference on Advanced in Control Engineering and Information Science . 2013

机译：Engel持续分数中部分和限制定理
5. Discrete local central limit theorems and boolean function complexity measures [D] . Gilmer, Justin. 2015

机译：离散局部中心极限定理和布尔函数复杂度测度
6. Almost sure central limit theorem for self-normalized products of the some partial sums of ... formula ...-mixing sequences [O] . Xili Tan, Wei Liu -1

机译：... ... ...-混合序列的部分和的自归一化产品的几乎确定中心极限定理
7. An almost sure central limit theorem for products of sums of partial sums under association [O] . Zhang Yong, Yang Xiao-Yun, Dong Zhi-Shan 2009

机译：关联下部分和的乘积的几乎确定的中心极限定理
8. The Equivalence of Functional Central Limit Theorems for Counting Processes and Associated Partial Sums [R] . Iglehart, D. L., Whitt, W. 1969

机译：计数过程和相关部分和的功能中心极限定理的等价性

The almost sure local central limit theorem for products of partial sums under negative association

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