IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v24y2021i2d10.1007_s11203-020-09234-0.html
   My bibliography  Save this article

Estimation of stopping times for stopped self-similar random processes

Author

Listed:
  • Viktor Schulmann

    (Technische Universität Dortmund)

Abstract

Let $$X=(X_t)_{t\ge 0}$$ X = ( X t ) t ≥ 0 be a known process and T an unknown random time independent of X. Our goal is to derive the distribution of T based on an iid sample of $$X_T$$ X T . Belomestny and Schoenmakers (Stoch Process Appl 126(7):2092–2122, 2015) propose a solution based the Mellin transform in case where X is a Brownian motion. Applying their technique we construct a non-parametric estimator for the density of T for a self-similar one-dimensional process X. We calculate the minimax convergence rate of our estimator in some examples with a particular focus on Bessel processes where we also show asymptotic normality.

Suggested Citation

  • Viktor Schulmann, 2021. "Estimation of stopping times for stopped self-similar random processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 477-498, July.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:2:d:10.1007_s11203-020-09234-0
    DOI: 10.1007/s11203-020-09234-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11203-020-09234-0
    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/s11203-020-09234-0?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. Belomestny, Denis & Schoenmakers, John, 2016. "Statistical inference for time-changed Lévy processes via Mellin transform approach," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2092-2122.
    2. Belomestny, Denis & Schoenmakers, John, 2015. "Statistical Skorohod embedding problem: Optimality and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 169-180.
    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. Belomestny, Denis & Schoenmakers, John, 2016. "Statistical inference for time-changed Lévy processes via Mellin transform approach," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2092-2122.
    2. P. Carr & A. Itkin & D. Muravey, 2022. "Semi-analytical pricing of barrier options in the time-dependent Heston model," Papers 2202.06177, arXiv.org.
    3. Shimizu, Yasutaka & Zhang, Zhimin, 2017. "Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 84-98.
    4. Gery Geenens, 2021. "Mellin–Meijer kernel density estimation on $${{\mathbb {R}}}^+$$ R +," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 953-977, October.

    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:sistpr:v:24:y:2021:i:2:d:10.1007_s11203-020-09234-0. 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.