关于极大值和极小值的几乎确定的中心极限定理

2011 International Conference on Mechatronic Science, Electric Engineering and Computer (MEC) Pub Date : 2011-09-23 DOI:10.1109/MEC.2011.6025877

Liu Ke, Ren Xiang, Jiang Huanjun

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引用次数: 2

摘要

在1/n Σk=1|rk|log k exp{γ|rk|log k}≪(log log n)−(1+ε)的条件下，我们证明了一个几乎确定的最大值和最小值中心极限定理:limn→∞1/log n Σnk=1 1/k I (Vk < mk≤mk≤μk)=e−T+η。

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Almost sure central limit theorem on maxima and minima

We prove an almost sure central limit theorem on maxima and minima: limn→∞ 1/log n Σⁿk=1 1/k I (Vk < mk ≤ Mk ≤ μk)=e^{− T+η} a.s. as the Stationary Gaussian sequence with covariance rn under the condition 1/n Σk=1|rk|log k exp{γ|rk|log k} ≪ (log log n)^−(1+ε)

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2011 International Conference on Mechatronic Science, Electric Engineering and Computer (MEC)

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