Limit theorems under nonlinear expectations dominated by sublinear expectations

TL;DR

This paper develops new limit theorems under nonlinear expectations dominated by sublinear expectations, providing a framework for understanding convergence and distributional limits in a nonlinear setting.

Contribution

It introduces a novel estimate for uniform integrability under sublinear expectations and establishes comprehensive limit theorems with fully nonlinear limit distributions.

Findings

Established limit theorems under nonlinear expectations

Derived a new estimate for uniform integrability

Analyzed a special case with positively homogeneous limit distributions

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.