The Annals of Probability

A Particular Case of Correlation Inequality for the Gaussian Measure

Gilles Hargé

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Abstract

Our purpose is to prove a particular case of a conjecture concerning the Gaussian measure of the intersection of two symmetric convex sets of $\mathbb{R}^n$. This conjecture states that the measure of the intersection is greater or equal to the product of the measures. In this paper, we prove the inequality when one of the two convex sets is a symmetric ellipsoid and the other one is simply symmetric. The general case is still open.

Article information

Source
Ann. Probab., Volume 27, Number 4 (1999), 1939-1951.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022874822

Digital Object Identifier
doi:10.1214/aop/1022874822

Mathematical Reviews number (MathSciNet)
MR1742895

Zentralblatt MATH identifier
0962.28013

Subjects
Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60E15: Inequalities; stochastic orderings

Keywords
Key words and phrases Gaussian measure correlation log-concavity semigroups

Citation

Hargé, Gilles. A Particular Case of Correlation Inequality for the Gaussian Measure. Ann. Probab. 27 (1999), no. 4, 1939--1951. doi:10.1214/aop/1022874822. https://projecteuclid.org/euclid.aop/1022874822


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References

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