| 任意随机多元函数序列的一类强偏差定理 |
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| 引用本文： | 王康康,章婷芳,黄辉林.任意随机多元函数序列的一类强偏差定理[J].数学杂志,2010,30(1). |
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| 作者姓名： | 王康康 章婷芳 黄辉林 |
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| 作者单位： | 1. 江苏科技大学数理学院,江苏,镇江,212003
2. 上海交通大学数学系,上海,200240 |
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| 基金项目： | 江苏省高校自然科学基础研究项目 |
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| 摘 要： | 本文通过概率空间上的任意测度与另一任意测度相比较,研究了任意随机多元函数序列普遍成立的一类强偏差定理.利用网微分法与分析运算法,获得了若干任意信源的Shannon-Mcmillan随机逼近定理,并将已有的关于随机多地函数序列及离散信源的结果加以推广.
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| 关 键 词： | Shannon-Mcmillan逼近定理 小偏差定理 任意信源 多元函数 相对熵密度 |
A CLASS OF STRONG DEVIATION THEOREMS FOR ARBITRARY STOCHASTIC MULTIVARIATE FUNCTION SEQUENCE |
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| WANG Kang-kang,ZHANG Ting-fang,HUANG Hui-lin.A CLASS OF STRONG DEVIATION THEOREMS FOR ARBITRARY STOCHASTIC MULTIVARIATE FUNCTION SEQUENCE[J].Journal of Mathematics,2010,30(1). |
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| Authors: | WANG Kang-kang ZHANG Ting-fang HUANG Hui-lin |
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| Institution: | WANG Kang-kang~1,ZHANG Ting-fang~1,HUANG Hui-lin~2 (1.School of Math., Phys.,Jiangsu University of Science , Technology,Zhenjiang 212003,China) (2.Dept.of Math.,Shanghai Jiaotong University,Shanghai 200240,China) |
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| Abstract: | In this article,a class of small-deviation theorems for the multivariate function sequence of arbitrary random variables is discussed by comparison between the measure P and the measure Q.By using differentiation on a net and analytical methods,some Shannon-Mcmillan approximation theorems for arbitrary information source are obtained and some known results for the random multivariate function sequence and the discrete information source are extended. |
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| Keywords: | Shannon-Mcmillan approximation theorem small deviation theorems arbitrary information source multivariate function relative entropy density |
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