Limit Laws of the Iterated Logarithm Under Sub-linear Expectations

Let $\{Y_n; n\ge 1\}$ be a sequence of independent and identically distributed random variables with mean zero in Peng's framework of the sub-linear expectation space $(Ω,\mathscr{H},\widehat{\mathbb E})$, and $S_n=\sum_{i=1}^nY_i$. In this paper, we establish a limit law of \begin{align*}\lim_{n\to