Some Researches On The Strong Deviation Theorems Concerning Moving Average Of Dependent Random Sequences

By the end of 1970 s,Professor Liu Wen and his collaborators have generalized the strong limit theorems in probability theory to the case of inequality,and established the strong deviation theorems of random sequence and then obtained a lot of valuable results.This paper,based on the previous studies,is considered different reference product distribution and studied a class of strong deviation theorems concerning moving average of the dependent random sequence under different reference product distribution.The basic idea of this paper is to introduce moving likelihood ratio and moving relative entropy as a random measure of the deviation between the joint distribution and reference product distribution of the dependent random sequence.By restricting the range of the moving relative entropy,a subset of the sample space is given,and on this subset,the upper and lower bound the moving average of the random sequence,i.e.,the strong deviation theorem.The main idea of the proof is to construct a moving likelihood ratio with one parameter,and to obtain the almost sure convergence expressing by inequalities,through using the classical Borel-Cantelli lemma and analytical methods.The whole paper is divided into six chapters.The first chapter is the introduction,which briefly introduces the background of this thesis,and the basic ideas and methods on studying the strong deviation theorems of the dependent random sequence.The second chapter briefly introduces the related basic theorems and concepts,as well as the main results related to this paper.In the third chapter,we firstly introduce the concepts of moving likelihood ratio and moving relative entropy,and then obtain some strong deviation theorems for the moving average of stochastically dominated random sequence,generalizing some existing results.The fourth chapter studies a class of strong deviation theorems for continuous sources based non-memory Gamma source.In the fifth chapter,further studies on a class of strong deviation theorems for the moving average of arbitrary dependent random sequences based on countable double and non-homogeneous Markov function are presented.The sixth chapter gives the summary and the prospect of this paper.