A Note on the Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Partial Sums of Certain Stationary Gaussian Sequences

Yuanfang Wang, Qunying Wu

College of Science, Guilin University of Technology, Guilin, China.

DOI: 10.4236/am.2014.510153                

Abstract

Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.

Keywords

Almost Sure Central Limit Theorem, Stationary Gaussian Sequence, Slowly Varying Functions at Infinity

Conflicts of Interest

The authors declare no conflicts of interest.

References

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