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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 23, Fasc. 1,
pages 139 - 152
 

AN ALMOST SURE LIMIT THEOREM FOR THE MAXIMA AND SUMS OF STATIONARY GAUSSIAN SEQUENCES

Marcin Dudziński

Abstract: Let X ,X ,... 1 2 be some standardized stationary Gaussian process and let us put:

sum k V~ -------- Mk = max(X1, ...,Xk), Sk = Xi, sk = Var(Sk). i=1
Our purpose is to prove an almost sure central limit theorem for the sequence (Mk, Sk/sk) under suitable normalization of Mk. 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.

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