Two laws of large numbers for sublinear expectations

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.