A Daniell-Kolmogorov theorem for supremum preserving upper probabilities
The paper investigates uncertain processes for which the given imprecise probability model is a possibility measure, interpreted as upper probabilities that are in particular supremum preserving. The aim of the paper is to prove, for such possibilistic processes, a counterpart to a fundamental result in the theory of stochastic processes, namely the Daniell-Kolmogorov theorem. To attain this purpose, the authors define a possibilistic process as a special family of possibilistic variables, and show how its possibility distribution functions can be constructed. The notions of inner and outer regularity for possibility measures are introduced and investigated. Within this framework, an analog for possibilistic processes (and possibility measures) of the well-known probabilistic Daniell-Kolmogorov theorem is proved, in the important special case that the variables assume values in compact spaces and that the possibility measures involved are regular.
scientific article; zbMATH DE number 1340677
scientific article