Almost sure central limit theorem for self-normalized products of the some partial sums of ρ− $\rho^{-}$-mixing sequences [PDF]
Journal of Inequalities and Applications, 2018 Let {X,Xn}n∈N $\{X, X_{n}\}_{n\in N}$ be a strictly stationary ρ− $\rho^{-}$-mixing sequence of positive random variables, under the suitable conditions, we get the almost sure central limit theorem for the products of the some partial sums (∏i=1kSk,i(k ...
Xili Tan, Wei Liu
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Almost Sure Central Limit Theorem for a Nonstationary Gaussian Sequence
Journal of Inequalities and Applications, 2010 Let be a standardized non-stationary Gaussian sequence, and let denote , . Under some additional condition, let the constants satisfy as for some and , for some , then, we have almost surely for any , where is the indicator function ...
Qing-pei Zang
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Almost Sure Central Limit Theorem for Product of Partial Sums of Strongly Mixing Random Variables
Journal of Inequalities and Applications, 2011 We give here an almost sure central limit theorem for product of sums of strongly mixing positive random variables.
Ye Daxiang, Wu Qunying
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The almost sure local central limit theorem for products of partial sums under negative association
Journal of Inequalities and Applications, 2018 Let {Xn,n≥1} $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with EX1=μ>0 $\mathrm{E}X_{1}=\mu>0$ and Var(X1 ...
Yuanying Jiang, Qunying Wu
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A Note on Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Sums
Journal of Inequalities and Applications, 2010 Let be a sequence of independent and identically distributed (i.i.d.) random variables and denote , . In this paper, we investigate the almost sure central limit theorem in the joint version for the maxima and sums. If for some numerical sequences ,
Fu Ke-ang, Zang Qing-pei, Wang Zhi-xiang
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Almost sure central limit theorem for products of sums of partial sums
Journal of Inequalities and Applications, 2016 Considering a sequence of i.i.d. positive random variables, for products of sums of partial sums we establish an almost sure central limit theorem, which holds for some class of unbounded measurable functions.
Fengxiang Feng, Dingcheng Wang
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The Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences
Journal of Applied Mathematics, 2013 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 ...
Yuanying Jiang, Qunying Wu
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Journal of Inequalities and Applications, 2019 The almost sure local central limit theorem is a general result which contains the almost sure global central limit theorem. Let {Xk,k≥1} $\{X_{k},k\geq 1\}$ be a strictly stationary negatively associated sequence of positive random variables.
Feng Xu, Binhui Wang, Yawen Hou
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Some limit theorems for ratios of order statistics from uniform random variables
Journal of Inequalities and Applications, 2017 In this paper, we study the ratios of order statistics based on samples drawn from uniform distribution and establish some limit properties such as the almost sure central limit theorem, the large deviation principle, the Marcinkiewicz-Zygmund law of ...
Shou-Fang Xu, Yu Miao
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Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences
Mathematics, 2020 In this paper, we prove the almost sure convergences for the maximum and minimum of nonstationary and stationary standardized normal vector sequences under some suitable conditions.
Zhicheng Chen +2 more
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