AN ALMOST SURE LIMIT THEOREM FOR THE MAXIMA AND SUMS OF
STATIONARY GAUSSIAN SEQUENCES
Abstract: Let
be some standardized stationary Gaussian process and let us
put:

Our purpose is to prove an almost sure central limit theorem for the sequence

under suitable normalization of

The investigations presented in this
paper extend the recent research of Csaki and Gonchigdanzan [1] and Dudziński
[2].
2000 AMS Mathematics Subject Classification: Primary 60F15; Secondary
60F05.
Key words and phrases: Extreme values, partial sums, almost sure central limit theorem,
dependent stationary Gaussian sequences.