Limit properties of exceedances point processes of scaled stationary gaussian sequences

• Autorzy: Hashorva E. , Peng Z. , Weng Z.
• Języki publikacji: EN

Abstrakty

EN

We derive the limiting distributions of exceedances point processes of randomly scaled weakly dependent stationary Gaussian sequences under some mild asymptotic conditions. In the literature analogous results are available only for contracted stationary Gaussian sequences. In this paper, we include additionally the case of randomly inflated stationary Gaussian sequences with a Weibullian type random scaling. It turns out that the maxima and minima of both contracted and inflated weakly dependent stationary Gaussian sequences are asymptotically independent.

Słowa kluczowe

EN

stationary Gaussian sequence; exceedances point processes; maxima; minima; joint limit distribution; random contraction; random scaling; Weibullian tail behaviour

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 1
• Strony: 45--59
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Hashorva E.

• Department of Actuarial Science, University of Lausanne, Quartier UNIL-Dorigny, Bâtiment Extranef, CH-1015 Lausanne, Switzerland

autor

Peng Z.

• School of Mathematics and Statistics, Southwest University, 400715 Chongqing, China

autor

Weng Z.

• Department of Actuarial Science, University of Lausanne, Quartier UNIL-Dorigny, Bâtiment Extranef, CH-1015 Lausanne, Switzerland

Bibliografia

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• [9] A. Hu, Z. Peng, and Y. Qi, Limit laws for maxima of contracted stationary Gaussian sequences, Metrika 70 (2009), pp. 279-295.
• [10] M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York 1983.
• [11] Z. Peng, J. Tong, and Z. Weng, Joint limit distributions of exceedances point processes and partial sums of Gaussian vector sequence, Acta Math. Sin. (Engl. Ser.) 28 (8) (2012), pp. 1647-1662.
• [12] V. I. Piterbarg, Asymptotic Methods in the Theory of Gaussian Processes and Fields, Transl. Math. Monogr., Vol 148, American Mathematical Society, Providence, RI, 1996.
• [13] S. I. Resnick, Extreme Values, Regular Variation, and Point Processes, Applied Probability. A Series of the Applied Probability Trust, Vol. 4, Springer, New York 1987.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).