SOME PROPERTIES OF CONVEX HULLS GENERATED BY HOMOGENEOUS POISSON POINT PROCESSES

IN AN UNBOUNDED CONVEX DOMAIN

A. V. NAGAEV

Institute of Mathematics and Informatics, Nicolas Copernicus University, Torun, Poland

(Received January 7, 1992; revised April 15, 1994)

Abstract. Let C(A) be the convex hull generated by a Poisson point process in an unbounded convex set A. A representation of A\C(A) as the union of curvilinear triangles with independent areas is established. In the case when A is a cone the properties of the representation are examined more completely. It is also indicated how to simulate C(A) directly without first simulating the process itself.

Key words and phrases: Vertex of convex hull, Poisson point process.