Boolean random functions

Abstract

The notion of Boolean random functions is considered which is a generalization of Boolean random closed sets. Their construction is based on the combination of a sequence of primary random functions by the operation ∨ (supremum) or ∧ (infimum), and their main properties (among which the supremum or infimum infinite divisibility) are given in the case of scalar random functions built on Poisson point processes. Examples of applications to the modeling of rough surfaces are given.