Limit theorems under nonlinear expectations dominated by sublinear expectations

Abstract

In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit distributions can be completely nonlinear. Finally, we study the limit theorem in a special case, where the limit distribution satisfies positive homogeneity.