Approximation of Sojourn Times of Gaussian Processes |
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Authors: | Dȩbicki Krzysztof Michna Zbigniew Peng Xiaofan |
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Affiliation: | 1.Mathematical Institute, University of Wroc?aw, pl. Grunwaldzki 2/4, 50-384, Wroc?aw, Poland ;2.Department of Mathematics and Cybernetics, Wroc?aw University of Economics, Wroc?aw, Poland ;3.School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 610054, China ; |
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Abstract: | We investigate the tail asymptotic behavior of the sojourn time for a large class of centered Gaussian processes X, in both continuous- and discrete-time framework. All results obtained here are new for the discrete-time case. In the continuous-time case, we complement the investigations of Berman (Commun Pure Appl Math 38(5):519–528, 1985a and Probab Theory Relat Fields 20(1):113–124, 1987) for non-stationary X. A by-product of our investigation is a new representation of Pickands constant which is important for Monte-Carlo simulations and yields a sharp lower bound for Pickands constant. |
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