Approximation of Sojourn Times of Gaussian Processes

Krzysztof Dȩbicki (), Zbigniew Michna () and Xiaofan Peng ()
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Krzysztof Dȩbicki: University of Wrocław
Zbigniew Michna: Wrocław University of Economics
Xiaofan Peng: University of Electronic Science and Technology of China

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 4, 1183-1213

Abstract: 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.

Keywords: Sojourn time; Occupation time; Exact asymptotics; Gaussian process; Locally stationary processes; Primary 60G15; Secondary 60G70 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-018-9667-7

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