On peeling procedure applied to a Poisson point process

Youri Davydov (1) , Alexender Nagaev (2) , Anne Philippe (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Faculty of Mathematics and Computer Science
3 LMJL - Laboratoire de Mathématiques Jean Leray

In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are tightly connected with empirical point processes and stable random vectors. Results are given about the limit shape of the convex hulls in the case of a discrete spectral measure. We give some numerical experiments to illustrate the peeling procedure for a more large class of Poisson point processes.

Mots clés: stable random vectors; convex hulls; Poisson point process; peeling procedure

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Youri Davydov, Alexender Nagaev, Anne Philippe. On peeling procedure applied to a Poisson point process. 2008. ⟨hal-00339232v2⟩