The von Bahr-Esseen type inequality under sub-linear expectations and applications

TL;DR

This paper establishes a von Bahr-Esseen type inequality for negatively dependent variables under sub-linear expectations and applies it to derive laws of large numbers and convergence results, extending classical probability theory into the sub-linear framework.

Contribution

It introduces a new inequality under sub-linear expectations for negatively dependent variables and applies it to improve laws of large numbers and convergence results.

Findings

Established a von Bahr-Esseen type inequality under sub-linear expectations.

Derived Kolmogorov type weak law of large numbers.

Proved complete convergence for weighted sums.

Abstract

Moment inequalities play important roles in probability limit theory and mathematical statistics. In this work, the von Bahr-Esseen type inequality for extended negatively dependent random variables under sub-linear expectations is established successfully. By virtue of the inequality, we further obtain the Kolmogorov type weak law of large numbers for partial sums and the complete convergence for weighted sums, which extend and improve corresponding results in sub-linear expectation space.