Almost sure central limit theorem for self-normalized partial sums of ρ−-mixing sequences

Let {X,Xn}n∈N be a weakly stationary sequence of ρ−-mixing random variables. We discussed the almost sure central limit theorem for the self-normalized partial sums Sn/βVn, where Sn=∑i=1nXi, Vn2=∑i=1nXi2, constant β>0. Our results generalize and improve those on almost sure central limit theorems obtained by previous authors from the independent case to ρ−-mixing sequences and from dk=1/k  to  dk=lnckclexp(lnαck),0≤α<1/2.