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


Fengxiang Feng, Xiang Zeng




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