IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v18y2005i4d10.1007_s10959-005-7530-6.html
   My bibliography  Save this article

On Powers of Stieltjes Moment Sequences, I

Author

Listed:
  • Christian Berg

    (University of Copenhagen)

Abstract

For a Bernstein function f the sequence s n =f(1)·...· f(n) is a Stieltjes moment sequence with the property that all powers s n c ,c>0 are again Stieltjes moment sequences. We prove that $$s_n^c$$ is Stieltjes determinate for c≤ 2, but it can be indeterminate for c>2 as is shown by the moment sequence $$(n!)^c$$ , corresponding to the Bernstein function f(s)=s. Nevertheless there always exists a unique product convolution semigroup $$(\rho_c)_{c 2 to prove that the distribution of the product of p independent identically distributed normal random variables is indeterminate if and only if p≥ 3

Suggested Citation

  • Christian Berg, 2005. "On Powers of Stieltjes Moment Sequences, I," Journal of Theoretical Probability, Springer, vol. 18(4), pages 871-889, October.
    • Handle: RePEc:spr:jotpro:v:18:y:2005:i:4:d:10.1007_s10959-005-7530-6
    DOI: 10.1007/s10959-005-7530-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-005-7530-6
    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/s10959-005-7530-6?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. P. Patie & A. Vaidyanathan, 2022. "Non‐classical Tauberian and Abelian type criteria for the moment problem," Mathematische Nachrichten, Wiley Blackwell, vol. 295(5), pages 970-990, May.
    2. Javier Cárcamo, 2017. "Maps Preserving Moment Sequences," Journal of Theoretical Probability, Springer, vol. 30(1), pages 212-232, March.
    3. Gwo Dong Lin & Jordan Stoyanov, 2015. "Moment Determinacy of Powers and Products of Nonnegative Random Variables," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1337-1353, December.
    4. Arista, Jonas & Rivero, Víctor, 2023. "Implicit renewal theory for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 262-287.

    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:jotpro:v:18:y:2005:i:4:d:10.1007_s10959-005-7530-6. 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.