The Strong Law Of Large Number And Complete Convergence Of Extended Negative Dependent Random Variables Under Sub-linear Expectations

The probability limit theory plays an important role in the development history of statistics as a branch of probability theory.In the research history of the limit theory,the strong law of large number and the complete convergence of sequence of random variables are very popular.And the study of the two theories lay a good foundation for the research of other theories.In order to solve the problems of super hedge,uncertainty and risk measurement,the concept of sub-linear expectations has been proposed by researchers.Sub-linear expectation is an extension of additive expectations in the classical probability space,so in this paper,it is meaningful to study the strong law of large number and the complete convergence of sequence of random variables under the sub-linear expectations space.They are the extensions of classical probability theory.This dissertation is based on the properties of END random variable under sub-linear expectations and some basic inequalities and using the method of study sub-linear expectations limit theory,mainly from the following several aspects to research work:Firstly,we study the strong law of large number of Marcinkicwicz of the END identically distributed random variable sequence.We use the properties of END random variables and some inequalities of capacity,as well as the research methods of sub-linear expectations space.The strong law of large number of Marcinkicwicz of the END differently distributed random variable sequence under sub-linear expectations are obtained.Secondly,we studies the complete convergence and complete moment convergence for weighted sums of END random variables under classical probability space.By the properties of weighted sequence,exponential inequality under the sub-linear expectations space and the capacity inequalities,we obtained the complete convergence and complete moment convergence for weighted sums of END random variables under sub-linear expectations,generalizing the results of classical probability space to the sub-linear expectations space.Finally,this dissertation study the the complete convergence for product sums of independent identi-cally distributed random variables.And we think that it is the application of the complete convergence for weighted sums of END random variables under sub-linear expectations,as well as using the Rosenthal,inequality and the properties of the product sums,independent random variables.