Moment bounds for IID sequences under sublinear expectations

TL;DR

This paper establishes moment bounds for IID sequences under sublinear expectations and demonstrates that the central limit theorem by Peng remains valid under these conditions.

Contribution

It introduces a moment inequality for IID sequences under sublinear expectations and confirms the CLT's applicability in this framework.

Findings

Established a moment inequality for IID sequences under sublinear expectations.

Proved the validity of Peng's CLT under sublinear expectations for certain functions.

Extended the understanding of probabilistic bounds in non-linear expectation settings.

Abstract

In this paper, with the notion of independent identically distributed (IID) random variables under sublinear expectations introduced by Peng [7-9], we investigate moment bounds for IID sequences under sublinear expectations. We can obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality, we get the following result: For any continuous function $\phi$ satisfying the growth condition $|\phi(x)|\leq C(1+|x|^p)$ for some $C>0$, $p\geq1$ depending on $\phi$, central limit theorem under sublinear expectations obtained by Peng [8] still holds.