Baum–Katz-type complete and complete moment convergence theorems for the maximum of partial sums under sub-linear expectations

Let {X,Xn;n≥0} be a sequence of independent and identically distributed random variables in a sub-linear expectation space (Ω,H,Ê). We establish Baum–Katz-type complete and complete moment convergence theorems for the maximum of partial sums in a sub-linear expectation space. Our results extend the corresponding complete convergence results of probability spaces to sub-linear expectation spaces.