任意随机多元函数序列的一类强偏差定理  

A CLASS OF STRONG DEVIATION THEOREMS FOR ARBITRARY STOCHASTIC MULTIVARIATE FUNCTION SEQUENCE

作　　者：王康康[1] 章婷芳[1] 黄辉林[2] 

机构地区：[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

出　　处：《数学杂志》2010年第1期91-100,共10页Journal of Mathematics

基　　金：江苏省高校自然科学基础研究项目(07KJD110048;09KJD110002)

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元函数序列及离散信源的结果加以推广.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.

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 

分 类 号：O211.6[理学—概率论与数理统计]