MAX-INFINITELY DIVISIBLE AND MAX-STABLE SAMPLE CONTINUOUS-PROCESSES

Conditions for a process ζ on a compact metric space S to be simultaneously max-infinitely divisible and sample continuous are obtained. Although they fall short of a complete characterization of such processes, these conditions yield complete descriptions of the sample continuous non-degenerate max-stable processes on S and of the infinitely divisible non-void random compact subsets of a Banach space under the operation of convex hull of unions. © 1990 Springer-Verlag.