Limit Theorems For Negatively Dependent Random Variables Sequences Under The Sub-linear Expectations

In classical probability theory,probability limit theory plays an important role.However,this additive assumption is not always plausible because the uncertain phenomenon can not be modeled using additive probability or ad-ditive expectation.Non-additive probability and non-additive expectation are useful tools for studying uncertainty in statistics,measure of risk,superhedg-ing in finance and non-linear stochastic calculus.Statisticians are devoted to investigating probability limit theory for the sub-linear expectation in a gen-eral function space in recent years.This paper is divided into four parts to study complete convergence and strong law of large numbers of weighted sums for negatively dependent random variables under the sub-linear expectations.In chapter one,research background and development trend of the prob-ability limit theory are introduced under the sub-linear expectation.At the same time,our method and main results of this paper are also introduced.In chapter two,definition of sub-linear expectation and some lemmas are introduced.In chapter three,complete convergence for weighted sums of negatively dependent random variables under the sub-linear expectations are obtained.In chapter four,strong law of large numbers for weighted sums of negative-ly dependent random variables under the sub-linear expectations are discussed.