Convergences And Uniform Integrability Of A Sequence Of Random Variables Under Sublinear Expectations

In this paper,we mainly discuss convergences,uniform integrability and uniform nonintegrability of a sequence of random variables under a sublinear expectation space(?,H,E),and prove some new results.Firstly,we recall several convergences of a se-quence of random variables and discuss the relationship between them.Under the assump-tion that the sublinear expectation has the monotone continuity property,we will prove that LP convergence is stronger than convergence in capacity,convergence in capacity is stronger than convergence in distribution and give some equivalent characterizations of convergence in distribution.Secondly,we introduce the definition of uniform integrability under sublinear expectations and present a necessary and sufficient condition.Finally,we give the definition of uniform nonintegrability under sublinear expectations in contrast with classical probabilities and present some characterizations on this notion.