JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (2): 50-57.doi: 10.6040/j.issn.1671-9352.0.2015.106

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Almost sure central limit theorem for self-normalized products of some partial sums of NA random variables

XU Feng, WU Qun-ying*   

  1. College of Science, Guilin University of Technology, Guilin 541004, Guangxi, China
  • Received:2015-03-12 Online:2016-02-16 Published:2016-03-11

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Abstract: Let {X,Xn}n∈N be a stationary sequence of NA positive random variables. We proved an almost sure central limit theorem for the self-normalized products of some partial sums(∏ki=1(Sk,i/((k-1)μ)))μ/(βVk), where β>0 was a constant, E(X)=μ, Sk,i=∑kj=1Xj-Xi, 1≤i≤k, V2k=∑ki=1(Xi-μ)2. The results generalize not only on the weigh of the almost sure central limit theorem but also in the range of random variables.

Key words: self-normalized, products of sums, almost sure central limit theorem, NA sequences

CLC Number: 

  • O211
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