Moderate Deviation Principle And Large Deviation Principle Of Order Statistics Based On M-Dependent Random Variables

It is well known that deviation theory is one of the hot issues in study of the probability theory.The large deviation principle,which was introduced from the 60 s of last century,investigates a kind of problem of ergodic property rate of convergence,through the development of many scholars,and it has been called an important branch in probability theory now.Many scholars have investigated widely for correlative nature of quantile independent identically distributed and order statistic.Predecessors have discussed for the moderate deviation,the large deviation and Cramér large deviation deeply,and studied them for general distribution F(x).In this paper,we will continue to study the moderate deviation and large deviation principle of order statistics,and the main research is based on the m-dependent sequence of random variables.The first chapter provides the introduction.In this chapter,we mainly introduce the study background,some research results of predecessors and the structure arrangement of this paper.Chapter 2 is an important part of this paper,which introduces our main research results.Firstly,we provide the moderate deviation of m-dependent strong stationary sequence of random variables order statistic,with Cramér theorem and in combination with H(?)lder inequality to prove,which to verify whether its moderate deviation can be used or not,and then provides three inference forms.In the third chapter,the existence of the large deviation of the m-dependent strong stationary random variables order statistic.According to the lemmas of predecessors and exponentially tight,we get the existence of the large deviation theory.In the fourth chapter,it is mainly to summarize the research problems and future prospects of this paper.