Informational assessment of large scale self-similarity in nonlinear random field models

Abstract Large-scale behavior of a wide class spatial and spatiotemporal processes is characterized in terms informational measures. Specifically, subordinated random fields defined by nonlinear transformations on the family homogeneous isotropic Lancaster–Sarmanov are studied under long-range dependence (LRD) assumptions. In case, it shown that Shannon mutual information between field components for infinitely increasing distance, which can be properly interpreted as measure large scale structural complexity diversity, has an asymptotic power law decay depends underlying LRD parameter scaled subordinating function rank. Sensitivity with respect to distortion induced deformation generalized form given divergence-based Rényi also analyzed. framework, infinite-dimensional approach adopted. The study large-scale then extended proposal functional formulation class, well information. Results illustrated, context geometrical analysis sample paths, considering some scenarios based Gaussian Chi-Square fields.