On moments of the maximum of normed partial sums of ρ -mixing random variables

Let {Xn,n≥1} be a sequence of identically distributed ρ-mixing random variables and set Sn=∑i=1nXi,n≥1. Under suitable mixing rate restriction, the sufficient and necessary conditions for the existence of the moments of supn≥1|Sn/n1/r|p(00) are given, which are same as that in the independent case.