IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v150y2022icp19-49.html
   My bibliography  Save this article

Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure

Author

Listed:
  • Rønn-Nielsen, Anders
  • Stehr, Mads

Abstract

We consider an infinitely divisible random field indexed by Rd, d∈N, given as an integral of a kernel function with respect to a Lévy basis with a Lévy measure having a regularly varying right tail. First we show that the tail of its supremum over any bounded set is asymptotically equivalent to the right tail of the Lévy measure times the integral of the kernel. Secondly, when observing the field over an appropriately increasing sequence of continuous index sets, we obtain an extreme value theorem stating that the running supremum converges in distribution to the Fréchet distribution.

Suggested Citation

  • Rønn-Nielsen, Anders & Stehr, Mads, 2022. "Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 19-49.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:19-49
    DOI: 10.1016/j.spa.2022.04.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922000886
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.04.007?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. Molchanov, Ilya & Strokorb, Kirstin, 2016. "Max-stable random sup-measures with comonotonic tail dependence," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2835-2859.
    2. Fred Espen Benth & Anca Pircalabu, 2018. "A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(1), pages 36-65, January.
    3. Zaoli Chen & Gennady Samorodnitsky, 2020. "Extreme Value Theory for Long-Range-Dependent Stable Random Fields," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1894-1918, December.
    4. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    5. Kristjana Ýr Jónsdóttir & Anders Rønn-Nielsen & Kim Mouridsen & Eva B. Vedel Jensen, 2013. "Lévy-based Modelling in Brain Imaging," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 511-529, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Danijel Grahovac & Péter Kevei, 2025. "Tail Behavior and Almost Sure Growth Rate of Superpositions of Ornstein–Uhlenbeck-type Processes," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-15, March.

    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. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Gamma Related Ornstein-Uhlenbeck Processes and their Simulation," Papers 2003.08810, arXiv.org.
    2. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.
    3. Lingohr, Daniel & Müller, Gernot, 2019. "Stochastic modeling of intraday photovoltaic power generation," Energy Economics, Elsevier, vol. 81(C), pages 175-186.
    4. Nicola Cufaro Petroni & Piergiacomo Sabino, 2019. "Fast Pricing of Energy Derivatives with Mean-reverting Jump-diffusion Processes," Papers 1908.03137, arXiv.org, revised Mar 2020.
    5. Piergiacomo Sabino, 2020. "Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives," Papers 2004.06786, arXiv.org.
    6. Zdeněk Zmeškal & Dana Dluhošová & Karolina Lisztwanová & Antonín Pončík & Iveta Ratmanová, 2023. "Distribution Prediction of Decomposed Relative EVA Measure with Levy-Driven Mean-Reversion Processes: The Case of an Automotive Sector of a Small Open Economy," Forecasting, MDPI, vol. 5(2), pages 1-19, May.
    7. Thomas Gkelsinis & Alex Karagrigoriou, 2020. "Theoretical Aspects on Measures of Directed Information with Simulations," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    8. Madan, Dilip B. & Wang, King, 2021. "The structure of financial returns," Finance Research Letters, Elsevier, vol. 40(C).
    9. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    10. Dimitrios D. Thomakos & Michail S. Koubouros, 2011. "The Role of Realised Volatility in the Athens Stock Exchange," Multinational Finance Journal, Multinational Finance Journal, vol. 15(1-2), pages 87-124, March - J.
    11. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    12. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    13. Vladimir Tsenkov, 2009. "Financial Markets Modelling," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 5, pages 87-96.
    14. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    15. Fred Espen Benth & Martin Groth & Rodwell Kufakunesu, 2007. "Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 347-363.
    16. Torben G. ANDERSEN & Tim BOLLERSLEV & Nour MEDDAHI, 2002. "Correcting The Errors : A Note On Volatility Forecast Evaluation Based On High-Frequency Data And Realized Volatilities," Cahiers de recherche 21-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    17. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    18. Audrino, Francesco & Corsi, Fulvio, 2010. "Modeling tick-by-tick realized correlations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2372-2382, November.
    19. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    20. Gonzalez, Jhonny & Moriarty, John & Palczewski, Jan, 2017. "Bayesian calibration and number of jump components in electricity spot price models," Energy Economics, Elsevier, vol. 65(C), pages 375-388.

    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:spapps:v:150:y:2022:i:c:p:19-49. 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/505572/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.