P. Terán
Distributions of random sets are hard to handle since, their values being sets instead of points, they are probability measures on a sigma-algebra which is a set of sets. Therefore the need for simpler functions characterizing the distribution is even more pressing than for random variables and vectors.
The existence of such a function was established by Choquet in 1953 in compact metric spaces, and by Matheron in 1975 in locally compact second countable Hausdorff spaces.
It is a long-standing open problem to generalize those results to the class of spaces which is central in modern probability: Polish spaces (complete separable metric spaces). But progress in that direction has been meager. In 1998, Nguyen and Nguyen found a counterexample to a specific way of generalizing. In 1999, Philippe, Debs and Jaffray proved the result in the specific case of random compact sets.
In this communication, the general problem for random closed sets will be solved in the affirmative.
Palabras clave / Keywords: characterization, probability distribution, random set
Programado
Sesión J01 Probabilidad y Aplicaciones
31 de mayo de 2018 09:00
Sala 4
