IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v34y2021i4d10.1007_s10959-020-01021-0.html
   My bibliography  Save this article

Self-Standardized Central Limit Theorems for Trimmed Lévy Processes

Author

Listed:
  • David M. Mason

    (University of Delaware)

Abstract

We prove under general conditions that a trimmed subordinator satisfies a self-standardized central limit theorem (SSCLT). Our basic tool is a powerful distributional approximation result of Zaitsev (Probab Theory Relat Fields 74:535–566, 1987). Among other results, we obtain as special cases of our subordinator result the recent SSCLTs of Ipsen et al. (Stoch Process Appl 130:2228–2249, 2020) for trimmed subordinators and a trimmed subordinator analog of a central limit theorem of Csörgő et al. (Probab Theory Relat Fields 72:1–16, 1986) for intermediate trimmed sums in the domain of attraction of a stable law. We then use our methods to prove a similar theorem for general Lévy processes.

Suggested Citation

  • David M. Mason, 2021. "Self-Standardized Central Limit Theorems for Trimmed Lévy Processes," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2117-2144, December.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:4:d:10.1007_s10959-020-01021-0
    DOI: 10.1007/s10959-020-01021-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-020-01021-0
    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/s10959-020-01021-0?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. R. A. Doney & R. A. Maller, 2002. "Stability and Attraction to Normality for Lévy Processes at Zero and at Infinity," Journal of Theoretical Probability, Springer, vol. 15(3), pages 751-792, July.
    2. Ipsen, Yuguang & Maller, Ross & Resnick, Sidney, 2020. "Trimmed Lévy processes and their extremal components," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2228-2249.
    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. Grahovac, Danijel, 2022. "Intermittency in the small-time behavior of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 187(C).
    2. Yuguang Fan, 2017. "Tightness and Convergence of Trimmed Lévy Processes to Normality at Small Times," Journal of Theoretical Probability, Springer, vol. 30(2), pages 675-699, June.
    3. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.

    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:34:y:2021:i:4:d:10.1007_s10959-020-01021-0. 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.