Some Strong Deviation Theorems For Information Sources And A Class Of Limit Theorems On An Extended Tree

The strong deviation theorems,which are also called the small deviation theorems(i.e.,the strong limit theorems represented by inequalities)are new type theorems established by using the notion of the likelihood ratio.In 1989,Professor LiuWen first applied an analytic technique in the study of a class of strong deviation theorems for a sequence of random variables!7'. Later,Professor LiuWen studied the Shannon-McMillan theorem in information theory by using the analytic technique and obtained some strong deviation theorems with respect to relative entropy density [UH2?. In this paper some strong deviation theorems for arbitrary discrete information sources and non-negative continuous information sources are obtained.In the proof we go on applying the analytic technique. In addition ,we study a class of limit theorems on an extended tree.This paper contains four chapters.In chapter l,we introduce the relative background on this paper and give some simple expressions of the work which have been studied.In chapter 2, a class of strong deviation theorems on arbitrary information sources are established by using the notion of relative entropy with respect to a nonhomogeneous Markov information sources.In chapter 3,a class of strong deviation theorems on the differential entropy are established by using the notion of relative entropy rate and relative entropy with respect to reference product distribution.In chapter 4,we extend the random selection system on the tree and give a class of theorems on frequencies of occurrences of states and ordered couples of states of selection subsequencies on the tree.