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Approximation of Sojourn Times of Gaussian Processes

Author

Listed:
  • Krzysztof Dȩbicki

    (University of Wrocław)

  • Zbigniew Michna

    (Wrocław University of Economics)

  • Xiaofan Peng

    (University of Electronic Science and Technology of China)

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.

Suggested Citation

  • Krzysztof Dȩbicki & Zbigniew Michna & Xiaofan Peng, 2019. "Approximation of Sojourn Times of Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1183-1213, December.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9667-7
    DOI: 10.1007/s11009-018-9667-7
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    References listed on IDEAS

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    1. Hüsler, J. & Piterbarg, V., 1999. "Extremes of a certain class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 257-271, October.
    2. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    3. Dëbicki, Krzysztof & Kisowski, Pawel, 2008. "A note on upper estimates for Pickands constants," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2046-2051, October.
    4. Long Bai & Krzysztof Dȩbicki & Enkelejd Hashorva & Li Luo, 2018. "On Generalised Piterbarg Constants," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 137-164, March.
    5. Enkelejd Hashorva & Jürg Hüsler, 2000. "Extremes of Gaussian Processes with Maximal Variance near the Boundary Points," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 255-269, September.
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