IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v95y2001i1p151-176.html
   My bibliography  Save this article

Applications of the continuous-time ballot theorem to Brownian motion and related processes

Author

Listed:
  • Schweinsberg, Jason

Abstract

Motivated by questions related to a fragmentation process which has been studied by Aldous, Pitman, and Bertoin, we use the continuous-time ballot theorem to establish some results regarding the lengths of the excursions of Brownian motion and related processes. We show that the distribution of the lengths of the excursions below the maximum for Brownian motion conditioned to first hit [lambda]>0 at time t is not affected by conditioning the Brownian motion to stay below a line segment from (0,c) to (t,[lambda]). We extend a result of Bertoin by showing that the length of the first excursion below the maximum for a negative Brownian excursion plus drift is a size-biased pick from all of the excursion lengths, and we describe the law of a negative Brownian excursion plus drift after this first excursion. We then use the same methods to prove similar results for the excursions of more general Markov processes.

Suggested Citation

  • Schweinsberg, Jason, 2001. "Applications of the continuous-time ballot theorem to Brownian motion and related processes," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 151-176, September.
    • Handle: RePEc:eee:spapps:v:95:y:2001:i:1:p:151-176
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(01)00097-7
    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. Konstantopoulos, Takis, 1995. "Ballot theorems revisited," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 331-338, September.
    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. Bertoin, Jean, 2004. "On small masses in self-similar fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 13-22, January.

    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. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
    2. Yuen, Fei Lung & Lee, Wing Yan & Fung, Derrick W.H., 2020. "A cyclic approach on classical ruin model," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 104-110.

    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:95:y:2001:i:1:p:151-176. 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/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.