IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/623.html
   My bibliography  Save this paper

A Note on Stochastic Dominance and Compactness

Author

Listed:
  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this work, we discuss completeness for the lattice orders of first and second order stochastic dominance. The main results state that, both, first and second order stochastic dominance induce Dedekind super complete lattices, i.e. lattices in which every bounded nonempty subset has a countable subset with identical least upper bound and greatest lower bound. Moreover, we show that, if a suitably bounded set of probability measures is directed (e.g. a lattice), then the supremum and infimum w.r.t. first or second order stochastic dominance can be approximated by sequences in the weak topology or in the Wasserstein-1 topology, respectively. As a consequence, we are able to prove that a sublattice of probability measures is complete w.r.t. first order stochastic dominance or second order stochastic dominance and increasing convex order if and only if it is compact in the weak topology or in the Wasserstein-1 topology, respectively. This complements a set of characterizations of tightness and uniform integrability, which are discussed in a preliminary section.

Suggested Citation

  • Nendel, Max, 2019. "A Note on Stochastic Dominance and Compactness," Center for Mathematical Economics Working Papers 623, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:623
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2937261/2937262
    File Function: First Version, 2019
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2019. "Submodular Mean Field Games. Existence and Approximation of Solutions," Center for Mathematical Economics Working Papers 621, Center for Mathematical Economics, Bielefeld University.
    2. Hu, Tien-Chung & Rosalsky, Andrew, 2011. "A note on the de La Vallée Poussin criterion for uniform integrability," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 169-174, January.
    3. Leskelä, Lasse & Vihola, Matti, 2013. "Stochastic order characterization of uniform integrability and tightness," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 382-389.
    4. Chandra, Tapas Kumar, 2015. "de La Vallée Poussin’s theorem, uniform integrability, tightness and moments," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 136-141.
    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. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2019. "Submodular Mean Field Games. Existence and Approximation of Solutions," Center for Mathematical Economics Working Papers 621, Center for Mathematical Economics, Bielefeld University.

    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. Chandra, Tapas K. & Hu, Tien-Chung & Rosalsky, Andrew, 2016. "On uniform nonintegrability for a sequence of random variables," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 27-37.
    2. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2019. "Submodular Mean Field Games. Existence and Approximation of Solutions," Center for Mathematical Economics Working Papers 621, Center for Mathematical Economics, Bielefeld University.
    3. Rosalsky, Andrew & Thành, Lê Vǎn, 2021. "A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 178(C).
    4. Chandra, Tapas Kumar, 2015. "de La Vallée Poussin’s theorem, uniform integrability, tightness and moments," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 136-141.
    5. Shutian Liu & Yuhan Zhao & Quanyan Zhu, 2022. "Herd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach," Dynamic Games and Applications, Springer, vol. 12(1), pages 183-213, March.
    6. Lasse Leskelä, 2022. "Ross’s second conjecture and supermodular stochastic ordering," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 213-215, April.
    7. Imkeller, Peter & Mastrolia, Thibaut & Possamaï, Dylan & Réveillac, Anthony, 2016. "A note on the Malliavin–Sobolev spaces," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 45-53.

    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:bie:wpaper:623. 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: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    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.