A note on decoupling of local and global behaviour for the Dagum random field

Self-affinity versus decoupling: this dichotomy represents a breakthrough with respect to the previous literature, that has grown under the dogma of self-affinity. The word decoupling refers to those correlation functions allowing to treat independently the Hausdorff–Besicovitch dimension and Hurst effect parameters. The former is a roughness measure associated to profiles or surfaces. The latter reflects possible persistent or antipersistent behaviours of the associated random process or random field. Thus, the decoupling philosophy opens new avenues for the analysis and interpretation of local and global properties of random fields. In this paper, we introduce a new class of isotropic correlation functions, called Dagum, show its permissibility on any n-dimensional space, and analyse its attitudes with respect to decoupling. Interesting aspects arise from an intensive simulation study, conducted in one and two dimensions. In particular, it seems that the decoupling attitude may depend on the space dimension.