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

DOI10.1016/S0304-4149(03)00084-XzbMath1075.60505MaRDI QIDQ2574597

Qui-Man Shao

Publication date: 29 November 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

fractional Brownian motionsmall ball problemGaussian correlation conjecture

Mathematics Subject Classification ID

Gaussian processes (60G15) Inequalities; stochastic orderings (60E15) Strong limit theorems (60F15)

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Lower tail probabilities for Gaussian processes., Lower functions and Chung's LILs of the generalized fractional Brownian motion, Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality, Exact uniform modulus of continuity for \(q\)-isotropic Gaussian random fields, Maximal Inequalities for Fractional Brownian Motion: An Overview, The moduli of non-differentiability for Gaussian random fields with stationary increments, The three-dimensional Gaussian product inequality, The Csörgő-Révész moduli of non-differentiability of fractional Brownian motion, Probabilities of randomly centered small balls and quantization in Banach spaces

Cites Work

• A note on small ball probability of a Gaussian process with stationary increments
• A Gaussian correlation inequality for symmetric convex sets
• A nonsymmetric correlation inequality for Gaussian measure
• On the Gaussian measure of the intersection
• New Gaussian estimates for enlarged balls
• Metric entropy and the small ball problem for Gaussian measures
• The small ball problem for the Brownian sheet
• Small values of Gaussian processes and functional laws of the iterated logarithm
• Itô-Wiener chaos expansion with exact residual and correlation, variance inequalities
• Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables
• A particular case of correlation inequality for the Gaussian measure
• Small ball probabilities of Gaussian fields
• Lower classes for fractional Brownian motion
• Inequalities of correlation type for symmetric stable random vectors
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• Existence of small ball constants for fractional Brownian motions
• On Certain Inequalities for Normal Distributions and their Applications to Simultaneous Confidence Bounds
• On Multivariate Normal Probabilities of Rectangles: Their Dependence on Correlations
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