IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v20y2018i4d10.1007_s11009-017-9594-z.html
   My bibliography  Save this article

The Joint Distribution of Running Maximum of a Slepian Process

Author

Listed:
  • Pingjin Deng

    (Nankai University
    University of Lausanne)

Abstract

Consider the Slepian process S defined by S(t) = B(t + 1) − B(t),t ∈ [0, 1] with B(t), t ∈ ℝ a standard Brownian motion. In this contribution we analyze the properties between the maximum m s = max 0 ≤ u ≤ s S ( u ) $m_{s}=\max \limits _{0\leq u\leq s}S(u)$ and the maximum m t = max 0 ≤ u ≤ t S ( u ) $m_{t}=\max \limits _{0\leq u\leq t}S(u)$ for 0 ≤ s

Suggested Citation

  • Pingjin Deng, 2018. "The Joint Distribution of Running Maximum of a Slepian Process," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1123-1135, December.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9594-z
    DOI: 10.1007/s11009-017-9594-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-017-9594-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-017-9594-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Abundo, Mario, 2016. "On the excursions of drifted Brownian motion and the successive passage times of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 176-182.
    3. Dieker, A.B., 2005. "Extremes of Gaussian processes over an infinite horizon," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 207-248, February.
    4. Wolfgang Bischoff & Frank Miller & Enkelejd Hashorva & Jürg Hüsler, 2003. "Asymptotics of a Boundary Crossing Probability of a Brownian Bridge with General Trend," Methodology and Computing in Applied Probability, Springer, vol. 5(3), pages 271-287, September.
    5. 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.
    6. Pingjin Deng, 2016. "The boundary non-Crossing probabilities for Slepian process," Papers 1608.01133, arXiv.org.
    7. Popivoda, Goran & Stamatović, Siniša, 2016. "Extremes of Gaussian fields with a smooth random variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 185-190.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pingjin Deng, 2016. "The joint distributions of running maximum of a Slepian processes," Papers 1609.04529, arXiv.org.
    2. Bai, Long, 2020. "Extremes of standard multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 159(C).
    3. Bai, Long & Luo, Li, 2017. "Parisian ruin of the Brownian motion risk model with constant force of interest," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 34-44.
    4. Krzysztof Dȩbicki, 2022. "Exact asymptotics of Gaussian-driven tandem queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 285-287, April.
    5. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Wang, Longmin, 2020. "Extremes of vector-valued Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5802-5837.
    6. De[combining cedilla]bicki, Krzysztof & Kisowski, Pawel, 2008. "Asymptotics of supremum distribution of [alpha](t)-locally stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2022-2037, November.
    7. Hüsler, Jürg & Piterbarg, Vladimir, 2008. "A limit theorem for the time of ruin in a Gaussian ruin problem," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2014-2021, November.
    8. Hüsler, Jürg & Zhang, Yueming, 2008. "On first and last ruin times of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1230-1235, August.
    9. Blanchet, Jose & Lam, Henry, 2013. "A heavy traffic approach to modeling large life insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 237-251.
    10. Bisewski, Krzysztof & Dȩbicki, Krzysztof & Kriukov, Nikolai, 2023. "Simultaneous ruin probability for multivariate Gaussian risk model," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 386-408.
    11. Ji, Lanpeng & Peng, Xiaofan, 2023. "Extreme value theory for a sequence of suprema of a class of Gaussian processes with trend," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 418-452.
    12. Debicki, K. & Kosinski, K.M. & Mandjes, M. & Rolski, T., 2010. "Extremes of multidimensional Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2289-2301, December.
    13. 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.
    14. Krzysztof Dȩbicki & Peng Liu & Zbigniew Michna, 2020. "Sojourn Times of Gaussian Processes with Trend," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2119-2166, December.
    15. Krzysztof Bisewski & Krzysztof Dȩbicki & Tomasz Rolski, 2022. "Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ H = 1," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 53-68, October.
    16. Cheng, Dan, 2016. "Excursion probability of certain non-centered smooth Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 883-905.
    17. Hüsler, J. & Piterbarg, V., 2004. "On the ruin probability for physical fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 315-332, October.
    18. 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.
    19. Hashorva, Enkelejd, 2019. "Approximation of some multivariate risk measures for Gaussian risks," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 330-340.
    20. Tang, Linjun & Zheng, Shengchao & Tan, Zhongquan, 2021. "Limit theorem on the pointwise maxima of minimum of vector-valued Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 176(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9594-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.