IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i9-10p840-847.html

Polar sets for anisotropic Gaussian random fields

Author

Listed:
  • Söhl, Jakob

Abstract

This paper studies polar sets for anisotropic Gaussian random fields, i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical metric associated with the Gaussian random field is dominated by an anisotropic metric. We deduce an upper bound for the hitting probabilities and conclude that sets with small Hausdorff dimension are polar. Moreover, the results allow for a translation of the Gaussian random field by a random field, that is independent of the Gaussian random field and whose sample functions are of bounded Hölder norm.

Suggested Citation

  • Söhl, Jakob, 2010. "Polar sets for anisotropic Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 840-847, May.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:9-10:p:840-847
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00030-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. repec:hum:wpaper:sfb649dp2006-034 is not listed on IDEAS
    2. Shota Gugushvili, 2009. "Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(3), pages 321-343.
    3. repec:hum:wpaper:sfb649dp2006-035 is not listed on IDEAS
    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. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.
    2. Schmisser, Émeline, 2019. "Non parametric estimation of the diffusion coefficients of a diffusion with jumps," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5364-5405.
    3. Kato, Kengo & Kurisu, Daisuke, 2020. "Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1159-1205.
    4. Kappus, Johanna & Reiß, Markus, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers 2010-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. repec:hum:wpaper:sfb649dp2012-016 is not listed on IDEAS
    6. Fabienne Comte & Valentine Genon-Catalot, 2010. "Non-parametric estimation for pure jump irregularly sampled or noisy Lévy processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 290-313.
    7. Mark Anthony Caruana, 2017. "Estimation of Lévy Processes via Stochastic Programming and Kalman Filtering," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1211-1225, December.
    8. Kappus, Johanna, 2012. "Nonparametric adaptive estimation of linear functionals for low frequency observed Lévy processes," SFB 649 Discussion Papers 2012-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    10. Zhang, Zhimin & Yang, Hailiang, 2014. "Nonparametric estimation for the ruin probability in a Lévy risk model under low-frequency observation," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 168-177.
    11. repec:hum:wpaper:sfb649dp2012-003 is not listed on IDEAS
    12. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 314-328.
    13. Fabienne Comte & Céline Duval & Valentine Genon-Catalot, 2014. "Nonparametric density estimation in compound Poisson processes using convolution power estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(1), pages 163-183, January.
    14. Nickl, Richard & Reiß, Markus, 2012. "A Donsker theorem for Lévy measures," SFB 649 Discussion Papers 2012-003, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Kappus, Johanna, 2014. "Adaptive nonparametric estimation for Lévy processes observed at low frequency," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 730-758.
    16. repec:hum:wpaper:sfb649dp2011-027 is not listed on IDEAS
    17. Söhl, Jakob, 2009. "Polar sets of anisotropic Gaussian random fields," SFB 649 Discussion Papers 2009-058, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

    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:eee:stapro:v:80:y:2010:i:9-10:p:840-847. 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/622892/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.