Strassen's law of the iterated logarithm under sub-linear expectations

We establish the Strassen’s law of the iterated logarithm for independent and identically distributed random variables with $\widehat{\mathbb{E}}[X_1]=\widehat{\mathcal{E}}[X_1]=0$ and $C_{\mathbb{V}}[X_1^2]<\mathrm{\infty }$ under sub-linear expectation space with a countably sub-additive capacity $\mathbb{V}$. We also show the LIL for upper capacity with $\sigma =\bar{\sigma }$ under some certain conditions.