IDEAS home Printed from https://ideas.repec.org/a/bpj/strimo/v21y2003i2-2003p171-184n5.html
   My bibliography  Save this article

Estimating the dimension of factors of diffusion processes

Author

Listed:
  • Pötzelberger Klaus

Abstract

We present consistency results for estimators of the box-counting dimension of the support of probability distributions. The box-counting dimension of the support E is defined via the covering number, i.e. the minimal cardinality of a cover of E consisting of cubes of fixed side-length. Accordingly the covering number of a sample allows the definition of an estimator of the box-counting dimension of E. Consistency results for arrays of probability distributions may be applied to the distributions of innovations of Itô processes and allow the construction of consistent estimators of the dimension of the factors, i.e. of the dimension of the Brownian motion driving the process.

Suggested Citation

  • Pötzelberger Klaus, 2003. "Estimating the dimension of factors of diffusion processes," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 171-184, February.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:2/2003:p:171-184:n:5
    DOI: 10.1524/stnd.21.2.171.19006
    as

    Download full text from publisher

    File URL: https://doi.org/10.1524/stnd.21.2.171.19006
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1524/stnd.21.2.171.19006?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. Cutler, C. D. & Dawson, D. A., 1989. "Estimation of dimension for spatially distributed data and related limit theorems," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 115-148, January.
    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. Spodarev, Evgeny & Straka, Peter & Winter, Steffen, 2015. "Estimation of fractal dimension and fractal curvatures from digital images," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 134-152.
    2. Denker, Manfred & Min, Aleksey, 2008. "A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 665-683, April.

    More about this item

    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:bpj:strimo:v:21:y:2003:i:2/2003:p:171-184:n:5. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.