IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v65y1996i1p31-53.html
   My bibliography  Save this article

On the number of high excursions of linear growth processes

Author

Listed:
  • Erhardsson, Torkel

Abstract

Uni- and bidirectional linear growth processes arise from a Poisson point process on R x [0, [infinity]) with intensity measure l x [Lambda] (where l = Lebesgue measure) in a certain way. They can be used to model how "growth" is initiated at random times from random points on the line and from each point proceeds at constant speed in one or both directions. Each finite interval will be completely "overgrown" after an a.s. finite time, a time which equals the maximum of a linear growth process on the interval. We give here, using the coupling version of the Stein Chen method, an upper bound for the total variation distance between the distribution of the number of excursions above a threshold z for a linear growth process in an interval of finite length L, and a Poisson distribution. The bound tends to 0 as L and z grow to x in a proper fashion. The general results are then applied to two specific examples.

Suggested Citation

  • Erhardsson, Torkel, 1996. "On the number of high excursions of linear growth processes," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 31-53, December.
    • Handle: RePEc:eee:spapps:v:65:y:1996:i:1:p:31-53
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(96)00097-X
    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.

    Citations

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


    Cited by:

    1. Erhardsson, Torkel, 2001. "Refined distributional approximations for the uncovered set in the Johnson-Mehl model," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 243-259, December.

    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:65:y:1996:i:1:p:31-53. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/505572/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.