RANDOM SETS - MODELS AND STATISTICS

This paper surveys aspects of the theory of random closed sets, focuss ing on issues of practical and current interest. First, some historica l remarks on this part of probability theory are made, where the impor tant role of Georges Matheron is emphasized. Then, fundamental charact eristics of the distribution of random closed sets are introduced. The very important Boolean model serves as an example for discussing math ematical and statistical problems. A number of further models is then considered, namely excursion sets of random fields, the system of edge s of the Poisson Voronoi tessellation and various random systems of no n-overlapping spheres. Finally, some ideas of particle statistics are presented, including some models of random compact sets.