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Lithuanian Mathematical Journal

, Volume 53, Issue 4, pp 471–483 | Cite as

A general result on almost sure central limit theorem for self-normalized sums for mixing sequences*

  • Yong ZhangEmail author
Article

Abstract

Let X, X 1 , X 2 , . . . be a sequence of strictly stationary ϕ-mixing random variables with zero means. In this paper, we show that a self-normalized version of almost sure central limit theorem holds under the assumptions that the mixing coefficients satisfy \( \sum\nolimits_{n=1}^{\infty } {{\phi^{{{1 \left/ {2} \right.}}}}\left( {{2^n}} \right)<\infty } \); moreover, we no longer restrict ourselves to logarithmic averages, but allow rather arbitrary weight sequences.

Keywords

almost sure central limit theorem self-normalized sums ϕ-mixing 

MSC

60F15 60F05 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.College of MathematicsJilin UniversityChangchunPR China

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