Some properties of convex hulls generated by homogeneous Poisson point processes in an unbounded convex domain
type: Item
instance of: scholarly article
title: Some properties of convex hulls generated by homogeneous Poisson point processes in an unbounded convex domain
zbMATH Open document ID: 0829.60040
DOI: 10.1007/BF00773409
published in: Annals of the Institute of Statistical Mathematics
publication date: 1995-08-16T00:00:00Z
review text: Let \(A \subseteq \mathbb{R}^2\) be an unbounded convex set such that for all \(c \in \mathbb{R}\) the set \(A \cap \{(x,y) \mid y \leq c\}\) has finite area and let \(C(A)\) denote the convex hull generated by the restriction of a homogeneous Poisson point process in \(\mathbb{R}^2\) to the set \(A\). As the main result of this paper it is shown that the set \(A \backslash C(A)\) can be represented as the union of curvilinear triangles with independent, exponentially distributed areas. It is also indicated how to simulate \(C(A)\) directly without first simulating the process itself. In the case when \(A\) is a cone the properties of this representations are examined more completely.
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 786370
zbMATH Keywords: vertex of convex hull
zbMATH Keywords: Poisson point process
author: Alexander V. Nagaev
reviewed by: Peter Weiß
MaRDI profile type: Publication
cites work: An introduction to the theory of point processes
cites work: Limit theorems for convex hulls
cites work: Q3759605
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description: scientific article; zbMATH DE number 786370