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Simulation of Pickands constants

Author

Listed:
  • Krzysztof Burnecki
  • Zbigniew Michna

Abstract

Pickands constants appear in the asymptotic formulas for extremes of Gaussian processes. The explicit formula of Pickands constants does not exist. Moreover, in the literature there is no numerical approximation. In this paper we compute numerically Pickands constants by the use of change of measure technique. To this end we apply two different algorithms to simulate fractional Brownian motion. Finally, we compare the approximations with a theoretical hypothesis and a recently obtained lower bound on the constants. The results justify the hypothesis.

Suggested Citation

  • Krzysztof Burnecki & Zbigniew Michna, 2002. "Simulation of Pickands constants," HSC Research Reports HSC/02/03, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    • Handle: RePEc:wuu:wpaper:hsc0203
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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_02_03.pdf
    File Function: Final draft, 2002
    Download Restriction: no
    File URL: http://www.math.uni.wroc.pl/~pms/files/22.1/Article/22.1.14.pdf
    File Function: Final printed version, 2002
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    Citations

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    Cited by:

    1. Dëbicki, Krzysztof & Kisowski, Pawel, 2008. "A note on upper estimates for Pickands constants," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2046-2051, October.
    2. 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.

    More about this item

    Keywords

    Pickands constant; fractional Brownian motion; change of measure; Cholesky factorization; fGp algorithm;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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