A complete convergence theorem of the maximum of partial sums under the sub-linear expectations

Abstract

Let {X, Xn; n ≥ 0} be a sequence of independent and identically distributed random variables in a sub-linear expectation space (Ω, H, bE). We establish a complete convergence theorem of the maximum of partial sums max1≤j≤n Pij=1 Xi under optimal moment condition in a sub-linear expectation space. Our
result generalizes and improves the corresponding results.