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

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  • Xu, Feng
  • Wu, Qunying

Abstract

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.

Suggested Citation

  • Xu, Feng & Wu, Qunying, 2017. "Almost sure central limit theorem for self-normalized partial sums of ρ−-mixing sequences," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 17-27.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:17-27
    DOI: 10.1016/j.spl.2017.04.023
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    1. Peligrad, Magda & Shao, Qi-Man, 1995. "A note on the almost sure central limit theorem for weakly dependent random variables," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 131-136, February.
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