On the association of sum- and max-stable processes

We address the notion of association of sum- and max-stable processes from the perspective of linear and max-linear isometries. We establish the appealing result that these two classes of isometries can be identified on a proper space (the extended positive ratio space). This yields a natural way to associate to any max-stable process a sum-stable process. By using this association, we establish connections between structural and classification results for sum- and max-stable processes.