Un théorème d'unicité pour les hyperplans poissoniens
- 1 March 1974
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 11 (1) , 184-189
- https://doi.org/10.2307/3212596
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
This publication has 3 references indexed in Scilit:
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- Le théorème de représentation intégrale dans les ensembles convexes compactsAnnales de l'institut Fourier, 1960