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On the rose of intersections of stationary flat processes

Published online by Cambridge University Press:  01 July 2016

Eugene Spodarev*
Affiliation:
Friedrich-Schiller-Universität Jena
*
Postal address: Friedrich-Schiller-Universität Jena, Institut für Stochastik, Ernst-Abbe Platz 1-4, 07743 Jena, Germany. Email address: [email protected]

Abstract

The paper yields retrieval formulae of the directional distribution of a stationary k-flat process in ℝd if its rose of intersections with all r-flats is known. Cases k = d −1, 1 ≤ rd - 1 for arbitrary d and d = 4, k = 2, r = 2 are considered. Some generalizations to manifold processes in ℝd are made. The proofs use the methods of harmonic analysis on higher Grassmannians (spherical harmonics, integral transforms).

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 2001 

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