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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
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    References listed on IDEAS

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    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.
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    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).

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