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Quelques théorèmes centraux limites pour les processus poissoniens de droites dans le plan

Part of: Geometric probability and stochastic geometry Nonparametric inference Limit theorems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Katy Paroux
Katy Paroux*
Affiliation:
Université Lyon I
*
∗ Postal address: Laboratoire de Probabilités, Université Claude Bernard Lyon I, Bât. 101, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France. Email address: paroux@jonas.univ-lyon1.fr
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Abstract

We prove central limit theorems for certain geometrical characteristics of the convex polygons determined by a standard Poisson line process in the plane, such as: the angles at the vertices of the polygons, the empirical mean of the number of vertices and the empirical mean of the perimeter of the polygons.

Keywords

Processus poissonien de droitesthéorème central limitedistribution empirique

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60F05: Central limit and other weak theorems 60G57: Random measures 62G30: Order statistics; empirical distribution functions
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 3 , September 1998 , pp. 640 - 656
Copyright
Copyright © Applied Probability Trust 1998 

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