IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i2p195-200.html
   My bibliography  Save this article

Limit theorem for derivative martingale at criticality w.r.t branching Brownian motion

Author

Listed:
  • Yang, Ting
  • Ren, Yan-Xia

Abstract

We consider a branching Brownian motion on in which one particle splits into 1+X children. There exists a critical value in the sense that is the lowest velocity such that a traveling wave solution to the corresponding Kolmogorov-Petrovskii-Piskunov equation exists. It is also known that the traveling wave solution with velocity is closely connected with the rescaled Laplace transform of the limit of the so-called derivative martingale . Thus special interest is put on the property of its limit . Kyprianou [Kyprianou, A.E., 2004. Traveling wave solutions to the K-P-P equation: alternatives to Simon Harris' probability analysis. Ann. Inst. H. Poincaré 40, 53-72.] proved that, if EX(log+X)2+[delta] 0 while if EX(log+X)2-[delta]=+[infinity]. It is conjectured that is non-degenerate if and only if EX(log+X)2

Suggested Citation

  • Yang, Ting & Ren, Yan-Xia, 2011. "Limit theorem for derivative martingale at criticality w.r.t branching Brownian motion," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 195-200, February.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:2:p:195-200
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00325-1
    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.

    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:81:y:2011:i:2:p:195-200. 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/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.