IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i9p2049-2063.html
   My bibliography  Save this article

Extremes of the time-average of stationary Gaussian processes

Author

Listed:
  • De[combining cedilla]bicki, Krzysztof
  • Tabis, Kamil

Abstract

We study the exact asymptotics of , as u-->[infinity], where and {Z(t):t>=0} is a centered stationary Gaussian process with covariance function satisfying some regularity conditions. As an application, we analyze the probability of buffer emptiness in a Gaussian fluid queueing system and the collision probability of differentiable Gaussian processes with stationary increments. Additionally, we find estimates for analogues of Piterbarg-Prisyazhnyuk constants, that appear in the form of the considered asymptotics.

Suggested Citation

  • De[combining cedilla]bicki, Krzysztof & Tabis, Kamil, 2011. "Extremes of the time-average of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2049-2063, September.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:9:p:2049-2063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911001141
    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. O'Connell, Neil & Unwin, Antony, 1992. "Collision times and exit times from cones: a duality," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 291-301, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tan, Zhongquan, 2013. "An almost sure limit theorem for the maxima of smooth stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2135-2141.

    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:spapps:v:121:y:2011:i:9:p:2049-2063. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.