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

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 search for a different version of it.

    References listed on IDEAS

    as
    1. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    2. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    3. 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.
    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. Johanna Kappus, 2012. "Nonparametric adaptive estimation of linear functionals for low frequency observed Lévy processes," SFB 649 Discussion Papers SFB649DP2012-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Richard Nickl & Markus Reiß, 2012. "A Donsker Theorem for Lévy Measures," SFB 649 Discussion Papers SFB649DP2012-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. 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.
    5. 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.
    6. 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.
    7. Jakob Sohl, 2012. "Confidence sets in nonparametric calibration of exponential L\'evy models," Papers 1202.6611, arXiv.org, revised Sep 2013.
    8. Rama Cont & Peter Tankov, 2009. "Constant Proportion Portfolio Insurance In The Presence Of Jumps In Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 379-401, July.
    9. Jakob Söhl, 2012. "Confidence sets in nonparametric calibration of exponential Lévy models," SFB 649 Discussion Papers SFB649DP2012-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Song, Seongjoo, 2010. "Lévy density estimation via information projection onto wavelet subspaces," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1623-1632, November.
    11. Jakob Söhl, 2014. "Confidence sets in nonparametric calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 18(3), pages 617-649, July.
    12. Denis Belomestny, 2009. "Spectral estimation of the fractional order of a Lévy process," SFB 649 Discussion Papers SFB649DP2009-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Trabs, Mathias, 2014. "On infinitely divisible distributions with polynomially decaying characteristic functions," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 56-62.
    14. Jakob Sohl & Mathias Trabs, 2012. "Option calibration of exponential L\'evy models: Confidence intervals and empirical results," Papers 1202.5983, arXiv.org, revised Oct 2012.
    15. Todorov, Viktor, 2021. "Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 671-705.
    16. Denis Belomestny & Mathias Trabs & Alexandre Tsybakov, 2017. "Sparse covariance matrix estimation in high-dimensional deconvolution," Working Papers 2017-25, Center for Research in Economics and Statistics.
    17. Todorov, Viktor, 2022. "Nonparametric jump variation measures from options," Journal of Econometrics, Elsevier, vol. 230(2), pages 255-280.
    18. Jacob Söhl & Mathias Trabs, 2012. "Option calibration of exponential Lévy models: Implementation and empirical results," SFB 649 Discussion Papers SFB649DP2012-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. Denis Belomestny & John Schoenmakers, 2010. "A jump-diffusion Libor model and its robust calibration," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 529-546.
    20. Belomestny Denis & Mathew Stanley & Schoenmakers John, 2009. "Multiple stochastic volatility extension of the Libor market model and its implementation," Monte Carlo Methods and Applications, De Gruyter, vol. 15(4), pages 285-310, January.

    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.