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A note on upper estimates for Pickands constants

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  • Dëbicki, Krzysztof
  • Kisowski, Pawel

Abstract

Pickands constants play a significant role in the extreme value theory of Gaussian processes. Recall that where {B[alpha](t),t>=0} is a fractional Brownian motion with Hurst parameter [alpha]/2 and [alpha][set membership, variant](0,2]. In this note we derive new upper bounds for and [alpha][set membership, variant](1,2]. The obtained results improve bounds given by Shao [Shao, Q.M., 1996. Bounds and estimators of a basic constant in extreme value theory of Gaussian processes. Statist. Sinica 6, 245-257].

Suggested Citation

  • Dëbicki, Krzysztof & Kisowski, Pawel, 2008. "A note on upper estimates for Pickands constants," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2046-2051, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2046-2051
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    References listed on IDEAS

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    1. Krzysztof Burnecki & Zbigniew Michna, 2002. "Simulation of Pickands constants," HSC Research Reports HSC/02/03, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    2. Debicki, Krzysztof, 2002. "Ruin probability for Gaussian integrated processes," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 151-174, March.
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    Cited by:

    1. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Ji, Lanpeng & Tabiś, Kamil, 2015. "Extremes of vector-valued Gaussian processes: Exact asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4039-4065.
    2. Liu, Peng & Ji, Lanpeng, 2017. "Extremes of locally stationary chi-square processes with trend," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 497-525.
    3. 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.
    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.

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