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On the speed of convergence of Piterbarg constants

Author

Listed:
  • Krzysztof Bisewski

    (University of Lausanne, UNIL-Dorigny)

  • Grigori Jasnovidov

    (Department of Steklov Mathematical Institute of Russian Academy of Sciences, 27 Fontanka)

Abstract

In this paper, we derive an upper bound for the difference between the continuous and discrete Piterbarg constants. Our result allows us to approximate the classical Piterbarg constants by their discrete counterparts using Monte Carlo simulations with an explicit error rate.

Suggested Citation

  • Krzysztof Bisewski & Grigori Jasnovidov, 2023. "On the speed of convergence of Piterbarg constants," Queueing Systems: Theory and Applications, Springer, vol. 105(1), pages 129-137, October.
    • Handle: RePEc:spr:queues:v:105:y:2023:i:1:d:10.1007_s11134-023-09882-y
    DOI: 10.1007/s11134-023-09882-y
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    References listed on IDEAS

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    1. Borovkov, Konstantin & Mishura, Yuliya & Novikov, Alexander & Zhitlukhin, Mikhail, 2018. "New and refined bounds for expected maxima of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 142-147.
    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.
    3. Krzysztof Dȩbicki & Enkelejd Hashorva, 2020. "Approximation of Supremum of Max-Stable Stationary Processes & Pickands Constants," Journal of Theoretical Probability, Springer, vol. 33(1), pages 444-464, March.
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