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SOME PROPERTIES OF CONVEX HULLS GENERATED

BY HOMOGENEOUS POISSON POINT PROCESSES

IN AN UNBOUNDED CONVEX DOMAIN

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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.

**Source**
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