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A Gaussian correlation inequality and its applications to the existence of small ball constant

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  • Shao, Qi-Man

Abstract

Let X1,...,Xn be jointly Gaussian random variables with mean zero. It is shown that [for all]x>0 and [for all]1[less-than-or-equals, slant]k 0 such that for any 0 0 and y>0. As an application, it is proved that the small ball constant for the fractional Brownian motion of order [alpha] exists.

Suggested Citation

  • Shao, Qi-Man, 2003. "A Gaussian correlation inequality and its applications to the existence of small ball constant," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 269-287, October.
    • Handle: RePEc:eee:spapps:v:107:y:2003:i:2:p:269-287
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    References listed on IDEAS

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    1. Szarek, Stanislaw J. & Werner, Elisabeth, 1999. "A Nonsymmetric Correlation Inequality for Gaussian Measure," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 193-211, February.
    2. Koldobsky, A. L. & Montgomery-Smith, S. J., 1996. "Inequalities of correlation type for symmetric stable random vectors," Statistics & Probability Letters, Elsevier, vol. 28(1), pages 91-97, June.
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    Cited by:

    1. Hinojosa-Calleja, Adrián, 2023. "Exact uniform modulus of continuity for q-isotropic Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 197(C).
    2. Junyi Zhang & Zimian Wang & Zhezhen Jin & Zhiliang Ying, 2023. "A Step-Wise Multiple Testing for Linear Regression Models with Application to the Study of Resting Energy Expenditure," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 163-192, April.
    3. Wang, Wensheng & Xiao, Yimin, 2019. "The Csörgő–Révész moduli of non-differentiability of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 81-87.

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