Electronic Communications in Probability

A Gaussian Correlation Inequality and its Applications to Small Ball Probabilities

Wenbo Li

Full-text: Open access

Abstract

We present a Gaussian correlation inequality which is closely related to a result of Schechtman, Schlumprecht and Zinn (1998) on the well-known Gaussian correlation conjecture. The usefulness of the inequality is demonstrated by several important applications to the estimates of small ball probability.

Article information

Source
Electron. Commun. Probab., Volume 4 (1999), paper no. 14, 111-118.

Dates
Accepted: 29 September 1999
First available in Project Euclid: 2 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456938436

Digital Object Identifier
doi:10.1214/ECP.v4-1012

Mathematical Reviews number (MathSciNet)
MR1741737

Zentralblatt MATH identifier
0937.60026

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60E15: Inequalities; stochastic orderings 60J65: Brownian motion [See also 58J65]

Keywords
Small ball probabilities Gaussian correlation inequality

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Li, Wenbo. A Gaussian Correlation Inequality and its Applications to Small Ball Probabilities. Electron. Commun. Probab. 4 (1999), paper no. 14, 111--118. doi:10.1214/ECP.v4-1012. https://projecteuclid.org/euclid.ecp/1456938436


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