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

DOI: 10.4236/am.2014.510153   PDF   HTML     2,865 Downloads   3,630 Views   Citations

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.

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Wang, Y. and Wu, Q. (2014) A Note on the Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Partial Sums of Certain Stationary Gaussian Sequences. Applied Mathematics, 5, 1598-1608. doi: 10.4236/am.2014.510153.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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