A note on Gaussian correlation inequalities for nonsymmetric sets

We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if A⊂Rd is convex and the origin 0∈A, then for any ball B centered at the origin, it holds γd(A∩B)≥γd(A)γd(B), where γd is the standard Gaussian measure on Rd. This generalizes Proposition 1 in [Cordero-Erausquin, Dario, 2002. Some applications of mass transport to Gaussian-type inequalities. Arch. Ration. Mech. Anal. 161, 257–269].

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Year of publication:	2012
Authors:	Lim, Adrian P.C. ; Luo, Dejun
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 1, p. 196-202
Publisher:	Elsevier
Subject:	Correlation inequality \| Gaussian measure \| Convexity \| Log-concavity \| Optimal transport

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040127