Two laws of large numbers for sublinear expectations

TL;DR

This paper establishes weak and strong laws of large numbers within the framework of sublinear expectations, extending classical probability results to more general, non-additive expectation settings.

Contribution

It introduces new laws of large numbers under sublinear expectations using notions of uncorrelatedness and independence, broadening their applicability.

Findings

Weak law of large numbers under sublinear expectation.

Strong law of large numbers with regularity conditions.

Applications in engineering and statistics for quality assessment.

Abstract

In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of independence for random variable sequences and regular property for sublinear expectations, we get a strong one. These results are helpful for the application of the law of large numbers in engineering and statistics such as to assess the level of product quality and to explain the relationship between the statistical distribution and the sample distribution.