IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i1p84-95.html
   My bibliography  Save this article

A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers

Author

Listed:
  • Castaing, Charles
  • Quang, Nguyen Van
  • Thuan, Nguyen Tran

Abstract

We consider a new family of convex weakly compact valued integrable random sets which is called an adapted array of convex weakly compact valued integrable random variables of type p (1⩽p⩽2). By this concept, more general laws of large numbers will be established. Some illustrative examples are provided.

Suggested Citation

  • Castaing, Charles & Quang, Nguyen Van & Thuan, Nguyen Tran, 2012. "A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 84-95.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:84-95
    DOI: 10.1016/j.spl.2011.08.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211002768
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2011.08.012?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. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
    2. Quang, Nguyen Van & Huan, Nguyen Van, 2009. "On the strong law of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1891-1899, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Quang, Nguyen Van & Giap, Duong Xuan, 2013. "Mosco convergence of SLLN for triangular arrays of rowwise independent random sets," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1117-1126.

    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. Son, Ta Cong & Thang, Dang Hung & Dung, Le Van, 2012. "Rate of complete convergence for maximums of moving average sums of martingale difference fields in Banach spaces," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1978-1985.
    2. Wang, Rongming & Wang, Zhenpeng, 1997. "Set-Valued Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 180-198, October.
    3. Ezzaki, Fatima & Tahri, Khalid, 2019. "Representation theorem of set valued regular martingale: Application to the convergence of set valued martingale," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    4. Quang, Nguyen Van & Nguyen, Pham Tri, 2015. "Some strong laws of large number for double array of random upper semicontinuous functions in convex combination spaces," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 85-94.
    5. Reza Ezzati & Shokrollah Ziari, 2012. "Approximation of fuzzy integrals using fuzzy bernstein polynomials," Fuzzy Information and Engineering, Springer, vol. 4(4), pages 415-423, December.
    6. Tito Homem-de-Mello, 2001. "Estimation of Derivatives of Nonsmooth Performance Measures in Regenerative Systems," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 741-768, November.
    7. López-Díaz, Miguel, 2006. "An indexed multivariate dispersion ordering based on the Hausdorff distance," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1623-1637, August.
    8. Jang, Lee-Chae & Kwon, Joong-Sung, 1998. "A uniform strong law of large numbers for partial sum processes of Banach space-valued random sets," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 21-25, May.
    9. Kosaku Takanashi, 2017. "Local Asymptotic Normality of Infinite-Dimensional Concave Extended Linear Models," Keio-IES Discussion Paper Series 2017-012, Institute for Economics Studies, Keio University.
    10. Fabián Flores-Bazán & Luis González-Valencia, 2021. "Characterizing Existence of Minimizers and Optimality to Nonconvex Quadratic Integrals," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 497-522, February.
    11. Bhowmik, Anuj, 2013. "Edgeworth equilibria: separable and non-separable commodity spaces," MPRA Paper 46796, University Library of Munich, Germany.
    12. Terán, Pedro, 2003. "A strong law of large numbers for random upper semicontinuous functions under exchangeability conditions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 251-258, November.
    13. De Simone, Anna & Graziano, Maria Gabriella, 2003. "Cone conditions in oligopolistic market models," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 53-73, February.
    14. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
    15. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.
    16. Tuan Nguyen Dinh, 2023. "Regularity of Multipliers for Multiobjective Optimal Control Problems Governed by Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 762-796, February.
    17. Guillermo Ayala & María Concepción López-Díaz & Miguel López-Díaz & Lucía Martínez-Costa, 2015. "Methods and Algorithms to Test the Hausdorff and Simplex Dispersion Orders with an R Package," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 661-675, September.
    18. Emmanuel Lepinette, 2020. "Random optimization on random sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 159-173, February.
    19. Jinping Zhang & Keming Zhang, 2022. "Portfolio selection models based on interval-valued conditional value at risk (ICVaR) and empirical analysis," Papers 2201.02987, arXiv.org, revised Jul 2022.
    20. Lopez-Diaz, Miguel & Rodriguez-Muniz, Luis J., 2007. "Influence diagrams with super value nodes involving imprecise information," European Journal of Operational Research, Elsevier, vol. 179(1), pages 203-219, May.

    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:eee:stapro:v:82:y:2012:i:1:p:84-95. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.