Exponential inequalities under sub-linear expectations with applications to strong law of large numbers

Abstract

In this paper, we give some exponential inequalities for extended independent random variables
under sub-linear expectations. As an application, we obtain the strong convergence rate $O(n^{-1/2}\ln^{1/2}n)$ for the strong law of large numbers under sub-linear expectations, which generalizes some corresponding ones under the classical linear expectations.