Random sets. A survey of results and applications
type: Item
instance of: scholarly article
title: Random sets. A survey of results and applications
zbMATH Open document ID: 0754.60019
DOI: 10.1007/BF01066685
published in: Ukrainian Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 58669
zbMATH Keywords: epi-graph
zbMATH Keywords: survey
zbMATH Keywords: random closed sets
zbMATH Keywords: Boolean models
zbMATH Keywords: capacity theory
zbMATH Keywords: weak convergence of random sets
zbMATH Keywords: stochastic optimization problems
author: Ilya S. Molchanov
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
cites work: Q5184230
cites work: Applied Stochastic Geometry: A Survey (Invited Paper)
cites work: Q3759605
cites work: Q3680652
cites work: Theory of capacities
cites work: On the Convergence in Distribution of Measurable Multifunctions (Random Sets) Normal Integrands, Stochastic Processes and Stochastic Infima
cites work: Random sets without separability
cites work: Q5666837
cites work: Survey of Measurable Selection Theorems
cites work: On the Distribution of the Expected Values of the Order Statistics
cites work: Expected convex hulls, order statistics, and Banach space probabilities
cites work: Almost sure limit sets of random samples in ℝd
cites work: On the variance of random sets
cites work: A strong law of large numbers for random compact sets
cites work: A central limit theorem for random sets
cites work: Q3906905
cites work: Q4162318
cites work: Q3313010
cites work: Convergence and existence of random set distributions
cites work: Regularly varying functions
cites work: Q3923365
cites work: Random Set Theory and Problems of Modeling
cites work: Q3906884
cites work: Q3768087
cites work: Q3472909
cites work: Q3349781
cites work: Q3694430
cites work: Estimation of the Size Distribution of Spherical Grains in the Boolean Model
cites work: Unbiased set-valued estimators with minimal risk
cites work: Q3026760
cites work: Q3730714
cites work: Q3239624
cites work: Q3782303
cites work: Weak Convergence of Set-Valued Functions and Control
cites work: Integrals, conditional expectations, and martingales of multivalued functions
cites work: Q3797944
cites work: Homecomings of Markov processes
cites work: Structure of strictly Markov marked random closed sets
description: scientific article; zbMATH DE number 58669