caa a22 4500 469068825 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF02773690 doi (NATIONALLICENCE)springer-10.1007/BF02773690 Norberg Tommy Department of Mathematics, Chalmers University of Technology The University of Göteborg, S-412 96, Göteborg, Sweden aut On the existence of ordered couplings of random sets — with applications [Elektronische Daten] [Tommy Norberg] Letψ andϕ be two given random closed sets in a locally compact second countable topological spaceS. (They need not be based on the same probability space.) The main result gives necessary and sufficient conditions on the distributions ofψ andϕ, for the existence of two random closed sets $$\hat \psi $$ and $$\hat \varphi $$ , based on the same probability space and such that their distributions coincide with those ofψ andϕ, resp., and $$\hat \psi \subseteq \hat \varphi $$ a.s. This coupling result tells us in particular when a probability distribution onS is selectionable w.r.t. (the distribution of) a random closed set. An existence result for realizable thinnings of a simple point process is obtained by specializing it to supports of random measures. The coupling result is extended to random variables in a countably based continuous poset. As examples we mention various kinds of random capacities — in particular random measures — and random compact (saturated) sets. Moreover, the extended result tells us when a probability distribution onS is selectionable w.r.t. the distribution of a random compact (saturated) set. Hebrew University, 1992 Israel Journal of Mathematics Springer-Verlag 77/3(1992-10-01), 241-264 0021-2172 77:3<241 1992 77 11856 https://doi.org/10.1007/BF02773690 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02773690 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Norberg Tommy Department of Mathematics, Chalmers University of Technology The University of Göteborg, S-412 96, Göteborg, Sweden aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 77/3(1992-10-01), 241-264 0021-2172 77:3<241 1992 77 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer