A Class Of Limit Theorems For Moving Average Of Dependent Random Sequence

This paper studies the strong law of large numbers, completely convergence,and thesmall deviation theorem between arbitrary information source and Markov informationsource of dependent random sequences.The text consists of four chapters.The first part of this paper is the introduction, which introduces the research back-ground and the development of the probability limit theory at home and abroad, andthen we describe the research purposes, significance and so on.In chapter2: Taking the condition of E(exp{t|X₁|^1/p}<∞,（p>1）get itspupper and lower limit of the form of END random variables.Meanwhile, we obtained the classical strong law of large numbers.In chapter3: Using Borel-Cantelli Lemma we prove the completely convergence formoving averages of END sequence and the Gauss sequence as the form,and finally, we find the completely convergence of pth quartile of generalized empiricaldistribution of END random sequence.In chapter4: Assuming the random sequence of probability measure Pis arbitrary,and Q is Markov measure about. We established a class of smalldeviation theorems of binary function of arbitrary information source by appling movinglikelihood ratio and moving relative entropy.In chapter5: Compendious summarize this article, and proposed the following ques-tion of this article studies, set of thinking.