| 关于滑动相对熵的若干极限性质 |
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| 引用本文： | 任园园,汪忠志.关于滑动相对熵的若干极限性质[J].数学的实践与认识,2021(5):244-249. |
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| 作者姓名： | 任园园 汪忠志 |
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| 作者单位： | 信阳学院数学与统计学院;安徽工业大学数理科学与工程学院 |
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| 基金项目： | 国家自然科学基金(11571142);安徽省高校自然科学重点研究项目(KJ2017A547,KJ2017A851)。 |
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| 摘 要： | 引入滑动似然比和滑动相对熵等概念,讨论了滑动相对熵的若干渐近性质.主要结果是,获得了随机变量任意状态的相对频率与滑动相对熵之间的关系,并且给出了滑动相对熵基于相对频率的上界的估计.作为推论,得到了随机序列滑动平均的强大数定理.
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| 关 键 词： | 滑动似然比 滑动相对熵 极限性质 |
On Some Limit Properties of Moving Relative Entropy |
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| REN Yuan-yuan,WANG Zhong-zhi.On Some Limit Properties of Moving Relative Entropy[J].Mathematics in Practice and Theory,2021(5):244-249. |
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| Authors: | REN Yuan-yuan WANG Zhong-zhi |
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| Institution: | (School of Mathematics and Statistics,Xinyang College,Xinyang 464000,China;School of mathematics Physics Science and Engineering,AnHui University of Technology,Ma’anshan 243002,China) |
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| Abstract: | In this paper,the moving likelihood ratio and moving relative entropy are introduced,and some asymptotic properties of the moving relative entropy are discussed.The main result is that we obtain the relationship between the relative frequency and the moving relative entropy of random variables in any state,and give the estimation of the upper bound of the moving relative entropy based on the relative frequency.As a corollary,the strong number theorem for moving average of random sequences is obtained. |
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| Keywords: | moving likelihood ratio moving relative entropy limiting property |
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