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Un théorème d'unicité pour les hyperplans poissoniens

Published online by Cambridge University Press:  14 July 2016

G. Matheron
G. Matheron*
Affiliation:
Centre de Morphologie Mathématique, Fontainebleau
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Abstract

A stationary Poisson process of hyperplanes in Rn is characterized (up to an equivalence) by the function θ such that θ(s) is the density of the Poisson point process induced on the straight lines with direction s. The set of these functions θ is a convex cone ℛ1, a basis of which is a simplex Θ, and a given function θ belongs to ℛ1 if and only if it is the supporting function of a symmetrical compact convex set which is a finite Minkowski sum of line segments or the limit of such finite sums. Another application is given concerning the tangential cone at h = 0 of a coveriance function.

Keywords

POISSON FLATSSIMPLEXNON ISOTROPIC COVARIANCECOMPACT CONVEX SETS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 184 - 189
Copyright
Copyright © Applied Probability Trust 1974 

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References

Bibliographie

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