Central Limit Theorem And Law Of Large Numbers For Dependent Sequence

Probability limit theory is the important content of the probability theory and mathematical statistics.In recent decades,the study of probability limit theory has attracted scholars gradually,and there will be more development in the future.To make the research more realistic,scholars begin to study proba-bility limit theory for dependent random variables.This paper is divided into three parts to study some properties for m-dependent sequence and associated sequence.In chapter one,research background and development trend of the prob-ability limit theory are introduced for dependent sequence.At the same time,our method and main results of this paper are also introduced.In chapter two,we assume partial sums SNn=(?).The limit dis-tribution of the sequence SNn and the order of approximation after suitable normalization are obtained.In this section,{X_k,k?1} is a stationary se-quence of m-dependent random variables with a common distribution.And Nn is a sequence of random number,which is independent of the sequence of random variables {X_k,A?1} for every n?1.In chapter three,under the Lipschitz condition,the law of large numbers for associated sequences is studied by a new method.Furthermore,we promote the weights dj=1/j to dj=log?j/j or dj=e(logj)?/j,and give the proofs of main results.