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 (?,H,?). We establish a complete convergence theorem of the maximum of partial sums max1?j?n |?j i=1 Xi| under optimal moment condition in a sub-linear expectation space. Our result generalizes and improves the corresponding results.