IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v15y1983i1p59-82.html
   My bibliography  Save this article

Local times for two-parameter Lévy processes

Author

Listed:
  • Vares, Maria E.

Abstract

In this article we study the problem of existence of jointly continuous local time for two-parameter Lévy processes. Here, 'local time' is understood in the sense of occupation density, kand by 2-parameter Lévy process we mean a process X = {Xz: z [epsilon] [0, +[infinity])2} with independent and stationary increments (over rectangles of the type (s, s'] x (t, t']). We prove that if X is -valued and its lower index is greater than one, then a jointly continuous (at least outside {(x,s,t): x = 0}) local time can be obtained via Berman's method. Also, we extend to 2-parameter processes a result of Getoor and Kesten for usual Lévy processes. Implications in terms of 'approximate local growth' of X are stated.

Suggested Citation

  • Vares, Maria E., 1983. "Local times for two-parameter Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 59-82, June.
    • Handle: RePEc:eee:spapps:v:15:y:1983:i:1:p:59-82
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(83)90021-2
    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. Khoshnevisan, Davar & Xiao, Yimin & Zhong, Yuquan, 2003. "Local times of additive Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 193-216, April.

    More about this item

    Statistics

    Access and download statistics

    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:15:y:1983:i:1:p:59-82. 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.