Note on an intermediate Baum-Katz theorems under sub-linear expectations

Abstract

We study the Hsu-Robbins-Erdös theorem to the case when all moments under sub-linear expectations exist, but the moment generating function does not, viz, we suppose that $C_v\left\{\exp \left\{{\left({\log }^{+}|X|\right)}^{\hat{I}}\pm \right\}\right\}<\infty$ for some $\hat{I}\pm >1$. We also investigate multi-index version.

7 pages