IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v32y2019i4d10.1007_s10959-018-0853-x.html
   My bibliography  Save this article

Lévy Subordinators in Cones of Fuzzy Sets

Author

Listed:
  • Jan Schneider

    (Wroclaw University of Science and Technology)

  • Roman Urban

    (Wroclaw University)

Abstract

The general problem of how to construct stochastic processes which are confined to stay in a predefined cone (in the one-dimensional but also multi-dimensional case also referred to as subordinators) is of course known to be of great importance in the theory and a myriad of applications. In this paper we see how this may be dealt with on the metric space of fuzzy sets/vectors: By first relating with each proper convex cone C in $$\mathbb {R}^{n}$$ R n a certain cone of fuzzy vectors $$C^*$$ C ∗ and subsequently using some very specific Banach space techniques we have been able to produce as many pairs $$(L^*_t, C^*)$$ ( L t ∗ , C ∗ ) of fuzzy Lévy processes $$L^*_t$$ L t ∗ and cones $$C^*$$ C ∗ of fuzzy vectors such that $$L^*_t$$ L t ∗ are $$C^*$$ C ∗ -subordinators.

Suggested Citation

  • Jan Schneider & Roman Urban, 2019. "Lévy Subordinators in Cones of Fuzzy Sets," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1909-1924, December.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:4:d:10.1007_s10959-018-0853-x
    DOI: 10.1007/s10959-018-0853-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-018-0853-x
    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/s10959-018-0853-x?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.

    References listed on IDEAS

    as
    1. Bongiorno, Enea G., 2012. "A note on fuzzy set-valued Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 827-832.
    2. Bañuelos, Rodrigo & DeBlassie, Dante, 2006. "The exit distribution for iterated Brownian motion in cones," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 36-69, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gajda, Janusz & Magdziarz, Marcin, 2014. "Large deviations for subordinated Brownian motion and applications," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 149-156.

    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:32:y:2019:i:4:d:10.1007_s10959-018-0853-x. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.