### Bernhard Schmelzer

## Characterizing joint distributions of random sets with an application to set-valued stochastic processes

### Abstract

By the Choquet theorem, distributions of random closed sets can be characterized by a certain class of set functions called capacity functionals. In this paper a generalization to the multivariate case is presented, that is, it is proved that the joint distribution of finitely many random sets can be characterized by a set function fulfilling certain properties. Furthermore, we use this result to formulate an existence theorem for set-valued stochastic processes.

### Keywords

Random set, Choquet Theorem, capacity functional, joint distribution, Daniell-Kolmogorov Theorem.

### Download area

The paper is available in the following formats:

### Authors’ addresses

Technikerstraße 13, A-6020 Innsbruck, Austria

### E-mail addresses