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October 1999 Gaussian Measures of Dilatations of Convex Symmetric Sets
Rafał Latała, Krzysztof Oleszkiewicz
Ann. Probab. 27(4): 1922-1938 (October 1999). DOI: 10.1214/aop/1022874821

Abstract

We prove that the inequality $\Psi^-1(\mu(tA))\geq t\Psi^-1(\mu(A))$ holds for any centered Gaussian measure $\mu$ on a separable Banach space $F$, any convex, closed, symmetric set $A\subset{F}$ and $t\geq1$, where $\Psi(x)=\gamma_1(-x,x)=(2\pi)^-1/2\int_{-x}^x\exp(-y^2)2)dy$. As an application, the best constants in comparison of moments of Gaussian vectors are calculated.

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Rafał Latała. Krzysztof Oleszkiewicz. "Gaussian Measures of Dilatations of Convex Symmetric Sets." Ann. Probab. 27 (4) 1922 - 1938, October 1999. https://doi.org/10.1214/aop/1022874821

Information

Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0966.60037
MathSciNet: MR20001H:60026
Digital Object Identifier: 10.1214/aop/1022874821

Subjects:
Primary: 60G15
Secondary: 60B11, 60E15

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • October 1999
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