IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-92324-6_3.html
   My bibliography  Save this book chapter

Lévy Processes in Homogeneous Spaces

In: Invariant Markov Processes Under Lie Group Actions

Author

Listed:
  • Ming Liao

    (Auburn University, Department of Mathematics and Statistics)

Abstract

Hunt’s generator formula for Lévy processes in a Lie group G holds also for Lévy processes in a homogeneous space G∕K, this will be discussed in §3.2, and some preparation will be dealt with in §3.1. Using this formula, it will be shown in §3.3 that a Lévy process in G∕K may be obtained as a projection of a Lévy process in G. As an application, some results on convolution semigroups on G and on G∕K will be derived in §3.4. In §3.4, we will also consider the problem of embedding an infinitely divisible distribution in a continuous convolution semigroup. A special class of Lévy processes in G or G∕K are Riemannian Brownian motions. Some related stochastic differential equations, and relations between Brownian motions in G and in G∕K, will be considered in §3.5.

Suggested Citation

  • Ming Liao, 2018. "Lévy Processes in Homogeneous Spaces," Springer Books, in: Invariant Markov Processes Under Lie Group Actions, chapter 0, pages 73-101, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-92324-6_3
    DOI: 10.1007/978-3-319-92324-6_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:sprchp:978-3-319-92324-6_3. 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.