Law of large numbers for <i>m</i>-dependent random vectors under sublinear expectations

Sublinear expectation relaxes the linear property of classical expectation to subadditivity and positive homogeneity, which can be expressed as $ \mathbb{E}(\cdot)=\sup_{\theta\in\Theta}E_{\theta}(\cdot) $ for a certain set of linear expectations $ \{E_{\theta}:\theta\in\Theta\} $. Such a framework can capture the uncertainty and facilitate a robust method of measuring risk loss reasonably. This study established a law of large numbers for m-dependent random vectors within the framework of sublinear expectation. Consequently, the corresponding explicit rate of convergence were derived. The results of this study can be considered as an extension of the Peng’s law of large numbers [22].