  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
results 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.
