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

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.