Stein's Method for Law of Large Numbers under Sublinear Expectations

TL;DR

This paper extends the law of large numbers under sublinear expectations by providing error estimates using Stein's method, enhancing understanding of convergence rates in this framework.

Contribution

It introduces Stein's method to quantify the error in the law of large numbers under sublinear expectations, which was not previously addressed.

Findings

Derived explicit error bounds for the law of large numbers under sublinear expectations.

Demonstrated the effectiveness of Stein's method in non-linear expectation settings.

Abstract

Peng, S. (\cite{P08b}) proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein's method.