IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v43y1992i2p291-301.html
   My bibliography  Save this article

Collision times and exit times from cones: a duality

Author

Listed:
  • O'Connell, Neil
  • Unwin, Antony

Abstract

We consider the first collision time for a set of independent one-dimensional zero-drift Wiener processes. For the 3-process problem, the first collision time corresponds to the first exit time of Brownian motion in a cone in 2, and we can apply the results of Spitzer (1958) and Dante DeBlassie (1987) to obtain its distribution. In the case where the processes have equal infinitesimal variance, a more elementary method yields nice closed-form results for the 3-process problem, and second order approximations for the general n-process problem. This case (for three processes) corresponds to Brownian motion in a cone of angle [pi]. The latter approach can in fact be applied to any system of independent (identical) Markov processes, provided the single-barrier hitting time distributions are known for the individual processes and their differences, and provided the processes can't jump over each other.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:43:y:1992:i:2:p:291-301
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(92)90063-V
    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. 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.

    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:43:y:1992:i:2:p:291-301. 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.