Abstract
LetC(A) be the convex hull generated by a Poisson point process in an unbounded convex setA. A representation ofA∖C(A) as the union of curvilinear triangles with independent areas is established. In the case whenA is a cone the properties of the representation are examined more completely. It is also indicated how to simulateC(A) directly without first simulating the process itself.
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Nagaev, A.V. Some properties of convex hulls generated by homogeneous Poisson point processes in an unbounded convex domain. Ann Inst Stat Math 47, 21–29 (1995). https://doi.org/10.1007/BF00773409
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DOI: https://doi.org/10.1007/BF00773409