General laws of large numbers under sublinear expectations

TL;DR

This paper extends classical laws of large numbers to the framework of sublinear expectations and capacities, providing three new laws under weaker conditions than previous results.

Contribution

It introduces three laws of large numbers under sublinear expectations that weaken the conditions required compared to prior work by Peng and Chen.

Findings

Extended laws of large numbers to non-additive probability measures

Provided weaker conditions for convergence under sublinear expectations

Generalized classical results to a broader mathematical framework

Abstract

In this paper, under some weaker conditions, we give three laws of large numbers under sublinear expectations (capacities), which extend Peng's law of large numbers under sublinear expectations in [8] and Chen's strong law of large numbers for capacities in [1]. It turns out that these theorems are natural extensions of the classical strong (weak) laws of large numbers to the case where probability measures are no longer additive.