Complete And Complete Integral Convergence For Arrays Of Rowwise Widely Negative Dependent Random Variables Under The Sub-linear Expectations

The limit theorem has far-reaching significance in the study of probability theory.So far,many scholars have studied it and obtained many excellent results.Complete convergence and complete moment convergence are two important branches.Due to the influence of the devel-opment of financial risk,super hedge pricing and other fields,the classic probability model has great limitations due to the additive assumptions,and many application fields are not established in the process of practice.Therefore,the study of the limit theorem under sub-linear expecta-tions has more practical application value and is also a current study hot pot.The development of complete convergence and complete moment convergence in the clas-sical probability theory is very complete,and many different forms of conclusions have been obtained.Different weighted sums and different random variables will result in different con-vergence properties.Widely negative dependent random variables include extended negative dependent random variables,negative dependent random variables,etc.,and are more extensive.Therefore,this article mainly focuses on the complete and complete moment convergence for weighted sums of arrays of rowwise widely negative dependent random variables,the original theorem is extended to the sub-linear expectation space through some new proof methods under the sub-linear expectations.In this article,first of all,we introduce the related concepts and properties under the sub-linear expectation space,and introduce the definition of arrays of rowwise widely negative de-pendent random variables under the sub-linear expectation framework.Then,we extend the complete moment convergence theorem in Wu et al.^[1]from the classic probability space to the sub-linear expectation space.Due to the requirement for theorem proof,we firstly need to im-prove the complete convergence theorem in Lin and Feng^[2]before this.Finally,we extend the complete convergence and complete moment convergence theorems in the paper of Ding et al.^[3]from the classical probability space to the sub-linear expectation space.