Random sets. A survey of results and applications. (English. Russian original) Zbl 0754.60019
Ukr. Math. J. 43, No. 12, 1477-1487 (1991); translation from Ukr. Mat. Zh. 43, No. 12, 1587-1599 (1991).
The paper consists of a survey on modern results in the theory of random closed sets. The emphasis is done on limit theorems and the law of large numbers for Minkowski sums and unions of random closed sets, Boolean models and their statistics, construction of distributions of random sets and related problems from the capacity theory. The survey contains a discussion on the weak convergence of random sets and its applications to epi-graphs of random functions and stochastic optimization problems. Some relations with the theory of random processes (level sets, multivalued random processes) are also mentioned.
Reviewer: I.S.Molchanov (Kiev)
MSC:
| 60D05 | Geometric probability and stochastic geometry |
Keywords:
epi-graph; survey; random closed sets; Boolean models; capacity theory; weak convergence of random sets; stochastic optimization problemsReferences:
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