An almost sure limit theorem for the maxima and sums of stationary Gaussian sequences

• Autorzy: Dudziński M.
• Języki publikacji: EN

Abstrakty

EN

Let X₁, X₂,… be some standardized stationary Gaussian process and let us put: M_k = max(X₁,…X_k), S_k = [wzór] X_i, σ_k = [wzór]. Our purpose is to prove an almost sure central limit theorem for the sequence (M_k, S_k/σ_k) under suitable normalization of M_k. The investigations presented in this paper extend the recent research of Csaki and Gonchigdanzan [1] and Dudziński [2].

Słowa kluczowe

EN

extreme values; partial sums; almost sure central limit theorem; dependent stationary Gaussian sequences

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 1
• Strony: 139--152
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Dudziński M.

• Department of Mathematics and Information Science, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warsaw, Poland

Bibliografia

• [1] E. Csaki and K. Gonchigdanzan, Almost sure limit theorem for the maximum of stationary Gaussian sequences, Statist. Probab. Lett. 58 (2002), pp. 195-203.
• [2] M. Dudziński, An almost sure maximum limit theorem for certain class of dependent stationary Gaussian sequences, Demonstratio Math. 35 (4) (2002), pp. 879-890.
• [3] H. C. Ho and T. Hsing, On the asymptotic joint distribution of the sum and maximum of stationary normal random variables, J. Appl. Probab. 33 (1996), pp. 138-145.
• [4] M. R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer, New York-Heidelberg-Berlin 1983.