The convergence rate for the laws of logarithms under sub-linear expectations

Abstract

Let $ \{X_n; n\geq1\} $ be a sequence of independent and identically distributed random variables in a sub-linear expectation space $ (\Omega, \mathcal{H}, \hat{\mathbb{E}}) $. The necessary and sufficient conditions for the convergence rate on the laws of the logarithms and the law of the iterated logarithm are obtained.

Keywords

• sub-linear expectation
• convergence rate
• laws of logarithms
• law of the iterated logarithm