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Limit theorems for convex hulls of random sets
Published online by Cambridge University Press: 01 July 2016
Abstract
Let , be i.i.d. random closed sets in . Limit theorems for their normalized convex hulls conv () are proved. The limiting distributions correspond to C-stable random sets. The random closed set A is called C-stable if, for any , the sets anA and conv ( coincide in distribution for certain positive an, compact Kn, and independent copies A1, …, An of A. The distributions of C-stable sets are characterized via corresponding containment functionals.
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- Copyright © Applied Probability Trust 1993
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