IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v25y2012i1d10.1007_s10959-010-0329-0.html
   My bibliography  Save this article

A Gaussian Inequality for Expected Absolute Products

Author

Listed:
  • Wenbo V. Li

    (University of Delaware)

  • Ang Wei

    (University of Rochester)

Abstract

We prove the inequality that ${\mathbb{E}}|X_{1}X_{2}\cdots X_{n}|\leq \sqrt{\mathrm{per}(\varSigma )}$ , for any centered Gaussian random variables X 1,…,X n with the covariance matrix Σ, followed by several applications and examples. We also discuss a conjecture on the lower bound of the expectation.

Suggested Citation

  • Wenbo V. Li & Ang Wei, 2012. "A Gaussian Inequality for Expected Absolute Products," Journal of Theoretical Probability, Springer, vol. 25(1), pages 92-99, March.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:1:d:10.1007_s10959-010-0329-0
    DOI: 10.1007/s10959-010-0329-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-010-0329-0
    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/s10959-010-0329-0?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. Vitale, R.A., 2008. "On the Gaussian representation of intrinsic volumes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1246-1249, August.
    2. Azaïs, Jean-Marc & Wschebor, Mario, 2008. "A general expression for the distribution of the maximum of a Gaussian field and the approximation of the tail," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1190-1218, July.
    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. Russell Oliver & Sun Wei, 2024. "Using sums-of-squares to prove Gaussian product inequalities," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-13.
    2. David Baños & Salvador Ortiz-Latorre & Andrey Pilipenko & Frank Proske, 2022. "Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise," Journal of Theoretical Probability, Springer, vol. 35(2), pages 714-771, June.
    3. Genest Christian & Ouimet Frédéric, 2022. "A combinatorial proof of the Gaussian product inequality beyond the MTP2 case," Dependence Modeling, De Gruyter, vol. 10(1), pages 236-244, January.
    4. Edelmann, Dominic & Richards, Donald & Royen, Thomas, 2023. "Product inequalities for multivariate Gaussian, gamma, and positively upper orthant dependent distributions," Statistics & Probability Letters, Elsevier, vol. 197(C).
    5. Russell, Oliver & Sun, Wei, 2022. "An opposite Gaussian product inequality," Statistics & Probability Letters, Elsevier, vol. 191(C).

    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. Lachièze-Rey, Raphaël, 2019. "Bicovariograms and Euler characteristic of random fields excursions," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4687-4703.
    2. Cheng, Dan, 2016. "Excursion probability of certain non-centered smooth Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 883-905.
    3. Azaïs, Jean-Marc & Delmas, Céline, 2022. "Mean number and correlation function of critical points of isotropic Gaussian fields and some results on GOE random matrices," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 411-445.
    4. Azaïs, Jean-Marc & Pham, Viet-Hung, 2016. "Asymptotic formula for the tail of the maximum of smooth stationary Gaussian fields on non locally convex sets," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1385-1411.
    5. Ang Wei, 2014. "Representations of the Absolute Value Function and Applications in Gaussian Estimates," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1059-1070, December.
    6. Volodko, Nadezhda V., 2014. "Small deviations of the determinants of random matrices with Gaussian entries," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 48-53.

    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:spr:jotpro:v:25:y:2012:i:1:d:10.1007_s10959-010-0329-0. 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.