关于树指标马氏双链随机矩阵的一个强偏差定理  

A Strong Deviation Theorem for the Stochastic Matrix of Double Markov Chains Indexed by a Tree

作　　者：金少华[1] 田雪然 王丽君 JIN Shaohua;TIAN Xueran;WANG Lijun(College of Science,Hebei University of Technology,Tianjin 300401,China;College of Data Science and Software Engineering,Baoding University,Baoding 071000,China)

机构地区：[1]河北工业大学理学院,天津300401 [2]保定学院数据科学与软件工程学院,河北保定071000

出　　处：《应用数学》2023年第4期922-928,共7页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11701139);河北省首批研究生教育教学改革研究项目(YJG2023020)。

摘　　要：本文研究树指标马氏双链随机矩阵的一个强偏差定理.首先给出非齐次树指标马氏双链样本相对熵率的概念,然后利用构造非负辅助鞅的方法,给出关于非齐次树指标马氏双链随机矩阵的一个强偏差定理.In this paper,a strong deviation theorem for the stochastic matrix of double Markov chains indexed by a tree is studied.Firstly the concept of relative entropy rate of samples of double Markov chains indexed by a non-homogeneous tree is given.Then by constructing non-negative auxiliary martingales,a strong deviation theorem for the stochastic matrix of double Markov chains indexed by a non-homogeneous tree is established.

关 键 词：强偏差定理 马氏双链 非齐次树 鞅 样本相对熵率 

分 类 号：O211.6[理学—概率论与数理统计]