IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v108y2024i3d10.1007_s11134-024-09925-y.html
   My bibliography  Save this article

Asymptotics for the Green’s functions of a transient reflected Brownian motion in a wedge

Author

Listed:
  • Sandro Franceschi

    (Institut Polytechnique de Paris, Télécom SudParis, Laboratoire SAMOVAR)

  • Irina Kourkova

    (Sorbonne Universite, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001)

  • Maxence Petit

    (Sorbonne Universite, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001)

Abstract

We consider a transient Brownian motion reflected obliquely in a two-dimensional wedge. A precise asymptotic expansion of Green’s functions is found in all directions. To this end, we first determine a kernel functional equation connecting the Laplace transforms of the Green’s functions. We then extend the Laplace transforms analytically and study its singularities. We obtain the asymptotics applying the saddle point method to the inverse Laplace transform on the Riemann surface generated by the kernel.

Suggested Citation

  • Sandro Franceschi & Irina Kourkova & Maxence Petit, 2024. "Asymptotics for the Green’s functions of a transient reflected Brownian motion in a wedge," Queueing Systems: Theory and Applications, Springer, vol. 108(3), pages 321-382, December.
    • Handle: RePEc:spr:queues:v:108:y:2024:i:3:d:10.1007_s11134-024-09925-y
    DOI: 10.1007/s11134-024-09925-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-024-09925-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-024-09925-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:spr:queues:v:108:y:2024:i:3:d:10.1007_s11134-024-09925-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.