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Intrinsic volumes and Gaussian processes

Part of: General convexity Distribution theory - Probability Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Richard A. Vitale
Richard A. Vitale*
Affiliation:
University of Connecticut
*
∗ Postal address: Department of Statistics, University of Connecticut, Storrs, CT 06269, USA. Email address: rvitale@uconnvm.uconn.edu
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Abstract

Intrinsic volumes are key functionals in convex geometry and have also appeared in several stochastic settings. Here we relate them to questions of regularity in Gaussian processes with regard to Itô–Nisio oscillation and metrization of GB/GC indexing sets. Various bounds and estimates are presented, and questions for further investigation are suggested. From alternate points of view, much of the discussion can be interpreted in terms of (i) random sets and (ii) properties of (deterministic) infinite-dimensional convex bodies.

Keywords

Convex bodydeviation boundGaussian processGB/GC setintrinsic volumeItô-Nisio oscillationmetricquermassintegralSteiner pointWills functional

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 52A07: Convex sets in topological vector spaces 52A22: Random convex sets and integral geometry 52A39: Mixed volumes and related topics 60D05: Geometric probability and stochastic geometry 60E15: Inequalities; stochastic orderings
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 354 - 364
Copyright
Copyright © Applied Probability Trust 2001 

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