IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v159y2020ics0167715219303438.html
   My bibliography  Save this article

Extremes of standard multifractional Brownian motion

Author

Listed:
  • Bai, Long

Abstract

Let SMBH(t),t∈(0,∞) be a standard multifractional Brownian motion(smBm), where H(t)∈(0,1) is a function of t. In this paper we derive the exact asymptotics of Psupt∈[T1,T2]SMBH(t)>u,u→∞for constants T1,T2≥0 and several forms of H(t).

Suggested Citation

  • Bai, Long, 2020. "Extremes of standard multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:stapro:v:159:y:2020:i:c:s0167715219303438
    DOI: 10.1016/j.spl.2019.108697
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219303438
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.108697?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. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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, 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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. 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.
    14. 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.
    15. Krzysztof Dȩbicki, 2022. "Exact asymptotics of Gaussian-driven tandem queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 285-287, April.
    16. Hüsler, Jürg & Piterbarg, Vladimir, 2004. "Limit theorem for maximum of the storage process with fractional Brownian motion as input," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 231-250, December.
    17. Long Bai & Peng Liu, 2019. "Drawdown and Drawup for Fractional Brownian Motion with Trend," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1581-1612, September.
    18. Pingjin Deng, 2016. "The joint distributions of running maximum of a Slepian processes," Papers 1609.04529, arXiv.org.
    19. 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.
    20. 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.

    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:eee:stapro:v:159:y:2020:i:c:s0167715219303438. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.