Law of Large Numbers and Central Limit Theorem Under Probability Uncertainty

Abstract

In this chapter, we first introduce two types of fundamentally important distributions, namely, maximal distribution and a new type of nonlinear normal distribution—G-normal distribution in the theory of sublinear expectations. The former corresponds to constants and the latter corresponds to normal distribution in the classical probability theory. We then present the law of large numbers (LLN) and central limit theorem (CLT) under sublinear expectations. It is worth pointing out that the limit in LLN is a maximal distribution and the limit in CLT is a G-normal distribution.