The Strong Deviation Theorems Conceirng Moving Average Of Dependent Random Vairables

This dissertation makes a main study of strong deviation theorems of any con-tinuous random variable moving average (namely the strong limit theorem with theinequality).The article is divided into four chapters.Introduction: We frst briefy introduce probability theory limit theory backgroundand development present situation. Secondly introduce the basic ideas and methodsof small deviation theorems of random variable Liuwen founded. Finally this chapterintroduces the random variable moving average、moving likelihood ratio and movingrelative entropy concept.The second chapter: We use the concept of random sequence moving likelihoodratio and moving relative entropy to study the random measurement of the deviationof the random sequence joint distribution and the reference distribution.A subset ofSample space is constructed with the moving relative entropy and we get a class ofstrong deviation theorems represented with inequalities on this subset,that is the smalldeviation theorem.The third chapter is devoted to a study of the limit property of the moving sumof dependent continuous non-negative random variable sequences.With the concept ofmoving likelihood ratio and the method of Laplace transformation,we obtain a kind ofstrong deviation theorems represented with inequalities i.e. the Small Deviation TheoremIn chapter4,we study the limit property of {1Bn(ξn), n≥1} for an arbitrary depen-dent continuous random variable sequence {ξn, n≥1} where {Bn, n≥1} is a sequence ofLebesgue sets of the real line and1Bnis the characteristic of Bnfor each n∈ω. A classof strong deviation theorem represented with inequalities is obtain.Moreover,we showthat the strong law of large numbers of {1Bn(ξn), n≥1}is an immediate consequence ofthe theorem in this section.