IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v38y2025i1d10.1007_s10959-024-01374-w.html
   My bibliography  Save this article

Tail Behavior and Almost Sure Growth Rate of Superpositions of Ornstein–Uhlenbeck-type Processes

Author

Listed:
  • Danijel Grahovac

    (J. J. Strossmayer University of Osijek)

  • Péter Kevei

    (University of Szeged)

Abstract

In this paper, we consider sample path growth of superpositions of Ornstein–Uhlenbeck-type processes (supOU). SupOU processes are stationary infinitely divisible processes defined as integrals with respect to a random measure. They allow marginal distributions and correlations to be modeled independently. Our results show that the almost sure behavior is primarily governed by the tail of the marginal distribution. In particular, we obtain a general integral test for the sample path growth that covers both heavy-tailed and light-tailed scenarios. We also investigate the tail behavior of the marginal distributions in connection with the characteristics of the underlying random measure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01374-w
    DOI: 10.1007/s10959-024-01374-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-024-01374-w
    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/s10959-024-01374-w?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Grahovac, Danijel & Leonenko, Nikolai N. & Taqqu, Murad S., 2019. "Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5113-5150.
    2. 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.
    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. Yoshioka, Hidekazu & Yoshioka, Yumi, 2025. "Stochastic volatility model with long memory for water quantity-quality dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).

    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. Grahovac, Danijel, 2022. "Intermittency in the small-time behavior of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 187(C).
    2. Danijel Grahovac & Nikolai N. Leonenko & Murad S. Taqqu, 2020. "The Multifaceted Behavior of Integrated supOU Processes: The Infinite Variance Case," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1801-1831, December.
    3. Jan Beran & Klaus Telkmann, 2021. "On inference for modes under long memory," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 429-455, June.
    4. Yoshioka, Hidekazu & Yoshioka, Yumi, 2025. "Stochastic volatility model with long memory for water quantity-quality dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01374-w. 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.