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

作者：Xu, Feng; Wu, Qunying^*

来源：Statistics & Probability Letters, 2017, 129: 17-27.

DOI：10.1016/j.spl.2017.04.023

• rho(-)-mixing sequences
• Self-normalized partial sums
• Almost sure central limit theorem

Let {X, X-n}(n is an element of N) be a weakly stationary sequence of rho(-)-mixing random variables. We discussed the almost sure central limit theorem for the self-normalized partial sums S-n/beta V-n, where S-n = Sigma(n)(i=1) X-i, V-n(2) = Sigma(n)(i=1) X-i(2), constant beta > 0. Our results generalize and improve those on almost sure central limit theorems obtained by previous authors from the independent case to rho(-)-mixing sequences and from d(k) = 1/k to d(k) = ln c(k)/c(l) exp(ln(alpha) c(k)), 0 less than or similar to alpha < 1/2.

• 出版日期2017-10
• 单位桂林理工大学; 暨南大学