Strassen’s Law of the Iterated Logarithm under Sub-linear Expectations

Abstract

We establish the Strassen’s law of the iterated logarithm (LIL for short) for independent and identically distributed random variables with \({\hat {\mathbb E}}[X_{1}]={\hat {\cal E}}[X_{1}]=0\) and \(C_{\mathbb V}[X_{1}^{2}]<\infty\) under a sub-linear expectation space with a countably sub-additive capacity \({\mathbb V}\). We also show the LIL for upper capacity with \(\sigma={\overline \sigma}\) under some certain conditions.