TITLE:
A Note on the Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Partial Sums of Certain Stationary Gaussian Sequences
AUTHORS:
Yuanfang Wang, Qunying Wu
KEYWORDS:
Almost Sure Central Limit Theorem, Stationary Gaussian Sequence, Slowly Varying Functions at Infinity
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.10,
June
9,
2014
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.