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On the rose of intersections of stationary flat processes

Part of: Integral transforms, operational calculus Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Eugene Spodarev
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]
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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 ≤ r ≤ d - 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).

Keywords

Grassmann manifoldsstationary flat (Poisson) processesmanifold processesspherical harmonics(spherical) Radon transformsine transformcosine transformrose of intersectionsstochastic geometry

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 44A12: Radon transform 44A99: None of the above, but in this section
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 3 , September 2001 , pp. 584 - 599
Copyright
Copyright © Applied Probability Trust 2001 

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