The Wills functional and Gaussian processes

DOI10.1214/aop/1041903224zbMath0879.60036OpenAlexW2071694869MaRDI QIDQ674527

Richard A. Vitale

Publication date: 22 January 1998

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1041903224

zbMATH Keywords

Gaussian processmixed volumeexponential boundintrinsic volumequermassintegralAlexandrov-Fenchel inequalitydeviation inequalitytail boundWills functional

Mathematics Subject Classification ID

Gaussian processes (60G15) Sample path properties (60G17) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (17)

Moment-entropy inequalities. ⋮ On the continuity of Pickands constants ⋮ Pickands-Piterbarg constants for self-similar Gaussian processes ⋮ A Dimension-Free Reverse Logarithmic Sobolev Inequality for Low-Complexity Functions in Gaussian Space ⋮ Concentration of the Intrinsic Volumes of a Convex Body ⋮ A strong law of large numbers on the harmonic \(p\)-combination ⋮ On the Gaussian representation of intrinsic volumes ⋮ On certain exponential regularity for Gaussian processes ⋮ Further inequalities for the (generalized) Wills functional ⋮ On bounded Gaussian processes ⋮ A transportation approach to the mean-field approximation ⋮ The Wills functional for Poisson processes ⋮ Convex geometry of max-stable distributions ⋮ Approximation of supremum of max-stable stationary processes \& Pickands constants ⋮ More on maximal inequalities for sub-fractional Brownian motion ⋮ On an exponential functional for Gaussian processes and its geometric foundations ⋮ Derivatives of sup-functionals of fractional Brownian motion evaluated at \(H=\frac{1}{2}\)

Cites Work

• Inequalities between intrinsic volumes
• Gaussian processes and mixed volumes
• Mesures cylindriques, espaces de Wiener et fonctions aléatoires gaussiennes
• A class of bounds for convex bodies in Hilbert space
• Zur Gitterpunktanzahl konvexer Mengen
• Non-linear angle-sum relations for polyhedral cones and polytopes
• Processus gaussiens et volumes mixtes
• On the volume of parallel bodies: a probabilistic derivation of the Steiner formula
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