IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v142y2006i1p187-21410.1007-s10479-006-6168-9.html
   My bibliography  Save this article

Epi-convergence almost surely, in probability and in distribution

Author

Listed:
  • Petr Lachout

Abstract

The paper deals with an epi-convergence of random real functions defined on a topological space. We follow the idea due to Vogel (1994) to split the epi-convergence into the lower semicontinuous approximation and the epi-upper approximation and localize them onto a given set. The approximations are shown to be connected to the miss- resp. hit-part of the ordinary Fell topology on sets. We introduce two procedures, called “localization”, separately for the miss-topology and the hit-topology on sets. Localization of the miss- resp. hit-part of the Fell topology on sets allows us to give a suggestion how to define the approximations in probability and in distribution. It is shown in the paper that in case of the finite-dimensional Euclidean space, the suggested approximations in probability coincide with the definition from Vogel and Lachout (2003). Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Petr Lachout, 2006. "Epi-convergence almost surely, in probability and in distribution," Annals of Operations Research, Springer, vol. 142(1), pages 187-214, February.
    • Handle: RePEc:spr:annopr:v:142:y:2006:i:1:p:187-214:10.1007/s10479-006-6168-9
    DOI: 10.1007/s10479-006-6168-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-006-6168-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-006-6168-9?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. G. Salinetti & W. Vervaat & R. J.-B. Wets, 1986. "On the Convergence in Probability of Random Sets (Measurable Multifunctions)," Mathematics of Operations Research, INFORMS, vol. 11(3), pages 420-422, August.
    2. Lisa A. Korf & Roger J.-B. Wets, 2001. "Random LSC Functions: An Ergodic Theorem," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 421-445, May.
    3. repec:ilo:ilowps:246575 is not listed on IDEAS
    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. Hess, Christian & Seri, Raffaello & Choirat, Christine, 2010. "Ergodic theorems for extended real-valued random variables," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1908-1919, September.
    2. Yanfang Zhang & Xiaojun Chen, 2014. "Regularizations for Stochastic Linear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 460-481, November.
    3. Sun, Ran & Fan, Yueyue, 2024. "Stochastic OD demand estimation using stochastic programming," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    4. Warren Powell & Andrzej Ruszczyński & Huseyin Topaloglu, 2004. "Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 814-836, November.
    5. Vogel Silvia, 2005. "Qualitative stability of stochastic programs with applications in asymptotic statistics," Statistics & Risk Modeling, De Gruyter, vol. 23(3), pages 219-248, March.

    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:annopr:v:142:y:2006:i:1:p:187-214:10.1007/s10479-006-6168-9. 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.