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Intersection densities of nonstationary Poisson processes of hypersurfaces

Part of: Geometric probability and stochastic geometry Stochastic processes General convexity

Published online by Cambridge University Press:  01 July 2016

Lars Michael Hoffmann
Lars Michael Hoffmann*
Affiliation:
Universität Karlsruhe (TH)
*
∗ Postal address: Institut für Algebra und Geometrie, Universität Karlsruhe (TH), 76128 Karlsruhe, Germany. Email address: lars.hoffmann@math.uni-karlsruhe.de
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Abstract

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Intersection densities are introduced for a large class of nonstationary Poisson processes of hypersurfaces and inequalities for them are proved. In doing so, similar results from both Wieacker (1986) and Schneider (2003) are summarized in one theorem and the concept of an associated zonoid of a Poisson process of hypersurfaces is generalized to a nonstationary setting.

Keywords

Poisson processintersection processhypersurfaceassociated zonoidSteiner convex set

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 39 , Issue 2 , June 2007 , pp. 307 - 317
Copyright
Copyright © Applied Probability Trust 2007 

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